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| bshanks@112 | 1 Introduction
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| bshanks@112 | 2 Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohisto-
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| bshanks@112 | 3 chemistry, in situ transgenic reporter, microarray voxelation, and others, allow the expression levels
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| bshanks@112 | 4 of many genes at many locations to be compared. Our goal is to develop automated methods to
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| bshanks@112 | 5 relate spatial variation in gene expression to anatomy. We want to find marker genes for specific
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| bshanks@96 | 6 anatomical regions, and also to draw new anatomical maps based on gene expression patterns.
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| bshanks@112 | 7 We will validate these methods by applying them to 46 anatomical areas within the cerebral cortex,
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| bshanks@112 | 8 by using the Allen Mouse Brain Atlas coronal dataset (ABA).
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| bshanks@112 | 9 This project has three primary goals:
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| bshanks@112 | 10 (1) develop an algorithm to screen spatial gene expression data for combinations of marker
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| bshanks@112 | 11 genes which selectively target anatomical regions.
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| bshanks@112 | 12 (2) develop an algorithm to suggest new ways of carving up a structure into anatomically dis-
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| bshanks@112 | 13 tinct regions, based on spatial patterns in gene expression.
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| bshanks@112 | 14 (3) adapt our tools for the analysis of multi/hyperspectral imaging data from the Geographic
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| bshanks@112 | 15 Information Systems (GIS) community.
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| bshanks@112 | 16 We will create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened
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| bshanks@112 | 17 version of the Allen Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical
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| bshanks@112 | 18 areas. We will use this dataset to validate the methods developed in (1) and (2). In addition to
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| bshanks@112 | 19 its use in neuroscience, this dataset will be useful as a sample dataset for the machine learning
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| bshanks@112 | 20 community.
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| bshanks@112 | 21 Although our particular application involves the 3D spatial distribution of gene expression, the
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| bshanks@112 | 22 methods we will develop will generalize to any high-dimensional data over points located in a low-
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| bshanks@112 | 23 dimensional space. In particular, our methods could be applied to the analysis of multi/hyperspectral
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| bshanks@112 | 24 imaging data, or alternately to genome-wide sequencing data derived from sets of tissues and dis-
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| bshanks@112 | 25 ease states.
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| bshanks@112 | 26 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The
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| bshanks@112 | 27 toolkit and the datasets will be published and freely available for others to use.
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| bshanks@112 | 28 __________________
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| bshanks@112 | 29 Background and related work
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| bshanks@112 | 30 Cortical anatomy
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| bshanks@112 | 31 The cortex is divided into areas and layers. Because of the cortical columnar organization, the
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| bshanks@112 | 32 parcellation of the cortex into areas can be drawn as a 2-D map on the surface of the cortex. In the
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| bshanks@112 | 33 third dimension, the boundaries between the areas continue downwards into the cortical depth,
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| bshanks@112 | 34 perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an
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| bshanks@112 | 35 area of the cortex as a slice of a six-layered cake1.
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| bshanks@112 | 36 It is known that different cortical areas have distinct roles in both normal functioning and in
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| bshanks@112 | 37 disease processes, yet there are no known marker genes for most cortical areas. When it is nec-
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| bshanks@112 | 38 essary to divide a tissue sample into cortical areas, this is a manual process that requires a skilled
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| bshanks@112 | 39 1Outside of isocortex, the number of layers varies.
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| bshanks@112 | 40 1
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| bshanks@112 | 41
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| bshanks@112 | 42 human to combine multiple visual cues and interpret them in the context of their approximate
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| bshanks@112 | 43 location upon the cortical surface.
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| bshanks@112 | 44 Even the questions of how many areas should be recognized in cortex, and what their arrange-
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| bshanks@112 | 45 ment is, are still not completely settled. A proposed division of the cortex into areas is called a
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| bshanks@112 | 46 cortical map. In the rodent, the lack of a single agreed-upon map can be seen by contrasting the
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| bshanks@120 | 47 recent maps given by Swanson[22] on the one hand, and Paxinos and Franklin[17] on the other.
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| bshanks@112 | 48 While the maps are certainly very similar in their general arrangement, significant differences re-
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| bshanks@112 | 49 main.
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| bshanks@112 | 50 The Allen Mouse Brain Atlas dataset
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| bshanks@120 | 51 The Allen Mouse Brain Atlas (ABA) data[14] were produced by doing in-situ hybridization on
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| bshanks@112 | 52 slices of male, 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice,
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| bshanks@112 | 53 and these pictures were semi-automatically analyzed to create a digital measurement of gene
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| bshanks@112 | 54 expression levels at each location in each slice. Per slice, cellular spatial resolution is achieved.
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| bshanks@112 | 55 Using this method, a single physical slice can only be used to measure one single gene; many
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| bshanks@112 | 56 different mouse brains were needed in order to measure the expression of many genes.
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| bshanks@120 | 57 Mus musculus is thought to contain about 22,000 protein-coding genes[27]. The ABA contains
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| bshanks@112 | 58 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured
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| bshanks@112 | 59 in coronal sections. Our dataset is derived from only the coronal subset of the ABA2. An auto-
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| bshanks@112 | 60 mated nonlinear alignment procedure located the 2D data from the various slices in a single 3D
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| bshanks@112 | 61 coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a
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| bshanks@120 | 62 side. There are 67x41x58 = 159,326 voxels, of which 51,533 are in the brain[16]. For each voxel
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| bshanks@120 | 63 and each gene, the expression energy[14] within that voxel is made available.
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| bshanks@120 | 64 The ABA is not the only large public spatial gene expression dataset[9][26][6][15][25][4][24][21][3].
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| bshanks@120 | 65 However, with the exception of the ABA, GenePaint[26], and EMAGE[25], most of the other re-
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| bshanks@112 | 66 sources have not (yet) extracted the expression intensity from the ISH images and registered the
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| bshanks@112 | 67 results into a single 3-D space.
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| bshanks@112 | 68 The remainder of the background section will be divided into three parts, one for each major
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| bshanks@112 | 69 goal.
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| bshanks@112 | 70 Goal 1, From Areas to Genes: Given a map of regions, find genes that mark those regions
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| bshanks@112 | 71 Machine learning terminology: classifiers The task of looking for marker genes for known
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| bshanks@112 | 72 anatomical regions means that one is looking for a set of genes such that, if the expression level
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| bshanks@112 | 73 of those genes is known, then the locations of the regions can be inferred.
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| bshanks@112 | 74 If we define the regions so that they cover the entire anatomical structure to be subdivided,
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| bshanks@112 | 75 and restrict ourselves to looking at one voxel at a time, we may say that we are using gene
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| bshanks@112 | 76 expression in each voxel to assign that voxel to the proper area. We call this a classification
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| bshanks@112 | 77 task, because each voxel is being assigned to a class (namely, its region). An understanding
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| bshanks@112 | 78 of the relationship between the combination of gene expression levels and the locations of the
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| bshanks@112 | 79 regions may be expressed as a function. The input to this function is a voxel, along with the gene
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| bshanks@112 | 80 expression levels within that voxel; the output is the regional identity of the target voxel, that is, the
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| bshanks@112 | 81 ____________________________________
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| bshanks@120 | 82 2The sagittal data do not cover the entire cortex, and also have greater registration error[16]. Genes were selected
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| bshanks@112 | 83 by the Allen Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc
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| bshanks@120 | 84 identification of a marked non-ubiquitous expression pattern”[16].
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| bshanks@112 | 85 2
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| bshanks@112 | 86
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| bshanks@112 | 87 region to which the target voxel belongs. We call this function a classifier. In general, the input to
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| bshanks@112 | 88 a classifier is called an instance, and the output is called a label (or a class label).
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| bshanks@112 | 89 Our goal is not to produce a single classifier, but rather to develop an automated method for
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| bshanks@112 | 90 determining a classifier for any known anatomical structure. Therefore, we seek a procedure by
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| bshanks@112 | 91 which a gene expression dataset may be analyzed in concert with an anatomical atlas in order to
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| bshanks@112 | 92 produce a classifier. The initial gene expression dataset used in the construction of the classifier
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| bshanks@112 | 93 is called training data. In the machine learning literature, this sort of procedure may be thought
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| bshanks@112 | 94 of as a supervised learning task, defined as a task in which the goal is to learn a mapping from
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| bshanks@112 | 95 instances to labels, and the training data consists of a set of instances (voxels) for which the labels
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| bshanks@112 | 96 (regions) are known.
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| bshanks@112 | 97 Each gene expression level is called a feature, and the selection of which genes3 to look at is
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| bshanks@112 | 98 called feature selection. Feature selection is one component of the task of learning a classifier.
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| bshanks@112 | 99 One class of feature selection methods assigns some sort of score to each candidate gene.
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| bshanks@112 | 100 The top-ranked genes are then chosen. Some scoring measures can assign a score to a set of
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| bshanks@112 | 101 selected genes, not just to a single gene; in this case, a dynamic procedure may be used in which
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| bshanks@112 | 102 features are added and subtracted from the selected set depending on how much they raise the
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| bshanks@112 | 103 score. Such procedures are called “stepwise” or “greedy”.
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| bshanks@112 | 104 Although the classifier itself may only look at the gene expression data within each voxel be-
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| bshanks@112 | 105 fore classifying that voxel, the algorithm which constructs the classifier may look over the entire
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| bshanks@112 | 106 dataset. We can categorize score-based feature selection methods depending on how the score
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| bshanks@112 | 107 of calculated. Often the score calculation consists of assigning a sub-score to each voxel, and
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| bshanks@112 | 108 then aggregating these sub-scores into a final score. If only information from nearby voxels is
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| bshanks@112 | 109 used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only information
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| bshanks@112 | 110 from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring
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| bshanks@112 | 111 method.
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| bshanks@112 | 112 Our Strategy for Goal 1
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| bshanks@112 | 113 Key questions when choosing a learning method are: What are the instances? What are the
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| bshanks@112 | 114 features? How are the features chosen? Here are four principles that outline our answers to these
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| bshanks@112 | 115 questions.
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| bshanks@112 | 116 Principle 1: Combinatorial gene expression
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| bshanks@112 | 117 It is too much to hope that every anatomical region of interest will be identified by a single
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| bshanks@112 | 118 gene. For example, in the cortex, there are some areas which are not clearly delineated by any
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| bshanks@112 | 119 gene included in the ABA coronal dataset. However, at least some of these areas can be delin-
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| bshanks@112 | 120 eated by looking at combinations of genes (an example of an area for which multiple genes are
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| bshanks@112 | 121 necessary and sufficient is provided in Preliminary Results, Figure 4). Therefore, each instance
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| bshanks@112 | 122 should contain multiple features (genes).
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| bshanks@112 | 123 Principle 2: Only look at combinations of small numbers of genes
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| bshanks@112 | 124 When the classifier classifies a voxel, it is only allowed to look at the expression of the genes
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| bshanks@112 | 125 which have been selected as features. The more data that are available to a classifier, the better
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| bshanks@112 | 126 that it can do. Why not include every gene as a feature? The reason is that we wish to employ the
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| bshanks@112 | 127 classifier in situations in which it is not feasible to gather data about every gene. For example, if we
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| bshanks@112 | 128 ____________________________________
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| bshanks@112 | 129 3Strictly speaking, the features are gene expression levels, but we’ll call them genes.
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| bshanks@112 | 130 3
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| bshanks@112 | 131
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| bshanks@112 | 132 want to use the expression of marker genes as a trigger for some regionally-targeted intervention,
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| bshanks@112 | 133 then our intervention must contain a molecular mechanism to check the expression level of each
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| bshanks@112 | 134 marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks
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| bshanks@112 | 135 the level of more than a handful of genes. Therefore, we must select only a few genes as features.
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| bshanks@112 | 136 The requirement to find combinations of only a small number of genes limits us from straightfor-
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| bshanks@112 | 137 wardly applying many of the most simple techniques from the field of supervised machine learning.
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| bshanks@112 | 138 In the parlance of machine learning, our task combines feature selection with supervised learning.
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| bshanks@112 | 139 Principle 3: Use geometry in feature selection
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| bshanks@112 | 140 When doing feature selection with score-based methods, the simplest thing to do would be
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| bshanks@112 | 141 to score the performance of each voxel by itself and then combine these scores (pointwise scor-
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| bshanks@112 | 142 ing). A more powerful approach is to also use information about the geometric relations between
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| bshanks@112 | 143 each voxel and its neighbors; this requires non-pointwise, local scoring methods. See Preliminary
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| bshanks@112 | 144 Results, figure 3 for evidence of the complementary nature of pointwise and local scoring methods.
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| bshanks@112 | 145 Principle 4: Work in 2-D whenever possible
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| bshanks@112 | 146 There are many anatomical structures which are commonly characterized in terms of a two-
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| bshanks@112 | 147 dimensional manifold. When it is known that the structure that one is looking for is two-dimensional,
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| bshanks@112 | 148 the results may be improved by allowing the analysis algorithm to take advantage of this prior
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| bshanks@112 | 149 knowledge. In addition, it is easier for humans to visualize and work with 2-D data.
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| bshanks@112 | 150 Goal 2, From Genes to Areas: given gene expression data, discover a map of regions
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| bshanks@101 | 151 Machine learning terminology: clustering
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| bshanks@112 | 152 If one is given a dataset consisting merely of instances, with no class labels, then analysis of
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| bshanks@112 | 153 the dataset is referred to as unsupervised learning in the jargon of machine learning. One thing
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| bshanks@112 | 154 that you can do with such a dataset is to group instances together. A set of similar instances is
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| bshanks@112 | 155 called a cluster, and the activity of grouping the data into clusters is called clustering or cluster
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| bshanks@112 | 156 analysis.
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| bshanks@112 | 157 The task of deciding how to carve up a structure into anatomical regions can be put into these
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| bshanks@112 | 158 terms. The instances are once again voxels (or pixels) along with their associated gene expression
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| bshanks@112 | 159 profiles. We make the assumption that voxels from the same anatomical region have similar gene
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| bshanks@112 | 160 expression profiles, at least compared to the other regions. This means that clustering voxels is
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| bshanks@112 | 161 the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into
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| bshanks@112 | 162 clusters of voxels with similar gene expression.
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| bshanks@112 | 163 It is desirable to determine not just one set of regions, but also how these regions relate to
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| bshanks@112 | 164 each other. The outcome of clustering may be a hierarchical tree of clusters, rather than a single
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| bshanks@112 | 165 set of clusters which partition the voxels. This is called hierarchical clustering.
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| bshanks@112 | 166 Similarity scores A crucial choice when designing a clustering method is how to measure
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| bshanks@112 | 167 similarity, across either pairs of instances, or clusters, or both. There is much overlap between
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| bshanks@112 | 168 scoring methods for feature selection (discussed above under Goal 1) and scoring methods for
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| bshanks@112 | 169 similarity.
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| bshanks@112 | 170 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene
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| bshanks@112 | 171 expression feature vector. By “dimension”, we mean the dimension of this vector, not the spatial
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| bshanks@112 | 172 4
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| bshanks@112 | 173
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| bshanks@112 | 174 dimension of the underlying data.
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| bshanks@112 | 175
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| bshanks@112 | 176
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| bshanks@104 | 177 Figure 1: Top row: Genes Nfic
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| bshanks@112 | 178 and A930001M12Rik are the most
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| bshanks@104 | 179 correlated with area SS (somatosen-
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| bshanks@112 | 180 sory cortex). Bottom row: Genes
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| bshanks@104 | 181 C130038G02Rik and Cacna1i are
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| bshanks@112 | 182 those with the best fit using logistic
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| bshanks@104 | 183 regression. Within each picture, the
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| bshanks@104 | 184 vertical axis roughly corresponds to
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| bshanks@104 | 185 anterior at the top and posterior at the
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| bshanks@104 | 186 bottom, and the horizontal axis roughly
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| bshanks@104 | 187 corresponds to medial at the left and
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| bshanks@104 | 188 lateral at the right. The red outline is
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| bshanks@104 | 189 the boundary of region SS. Pixels are
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| bshanks@104 | 190 colored according to correlation, with
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| bshanks@104 | 191 red meaning high correlation and blue
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| bshanks@112 | 192 meaning low. Unlike Goal 1, there is no externally-imposed need to
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| bshanks@112 | 193 select only a handful of informative genes for inclusion
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| bshanks@112 | 194 in the instances. However, some clustering algorithms
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| bshanks@112 | 195 perform better on small numbers of features4. There are
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| bshanks@112 | 196 techniques which “summarize” a larger number of fea-
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| bshanks@112 | 197 tures using a smaller number of features; these tech-
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| bshanks@112 | 198 niques go by the name of feature extraction or dimen-
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| bshanks@112 | 199 sionality reduction. The small set of features that such a
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| bshanks@112 | 200 technique yields is called the reduced feature set. Note
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| bshanks@112 | 201 that the features in the reduced feature set do not neces-
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| bshanks@112 | 202 sarily correspond to genes; each feature in the reduced
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| bshanks@112 | 203 set may be any function of the set of gene expression
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| bshanks@112 | 204 levels.
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| bshanks@112 | 205 Clustering genes rather than voxels Although the
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| bshanks@112 | 206 ultimate goal is to cluster the instances (voxels or pixels),
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| bshanks@112 | 207 one strategy to achieve this goal is to first cluster the
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| bshanks@112 | 208 features (genes). There are two ways that clusters of
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| bshanks@112 | 209 genes could be used.
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| bshanks@112 | 210 Gene clusters could be used as part of dimensionality
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| bshanks@112 | 211 reduction: rather than have one feature for each gene,
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| bshanks@112 | 212 we could have one reduced feature for each gene cluster.
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| bshanks@112 | 213 Gene clusters could also be used to directly yield a
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| bshanks@112 | 214 clustering on instances. This is because many genes
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| bshanks@112 | 215 have an expression pattern which seems to pick out a
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| bshanks@112 | 216 single, spatially contiguous region. This suggests the fol-
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| bshanks@112 | 217 lowing procedure: cluster together genes which pick out
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| bshanks@112 | 218 similar regions, and then to use the more popular com-
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| bshanks@112 | 219 mon regions as the final clusters. In Preliminary Results,
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| bshanks@112 | 220 Figure 7, we show that a number of anatomically recog-
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| bshanks@112 | 221 nized cortical regions, as well as some “superregions” formed by lumping together a few regions,
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| bshanks@112 | 222 are associated with gene clusters in this fashion.
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| bshanks@112 | 223 Goal 3: interoperability with multi/hyperspectral imaging analysis software
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| bshanks@112 | 224 A typical color image associates each pixel with a vector of three values. Multispectral and hyper-
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| bshanks@112 | 225 spectral images, however, are images which associate each pixel with a vector containing many
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| bshanks@112 | 226 values. The different positions in the vector correspond to different bands of electromagnetic
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| bshanks@112 | 227 wavelengths5.
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| bshanks@112 | 228 Some analysis techniques for hyperspectral imaging, especially preprocessing and calibration
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| bshanks@112 | 229 techniques, make use of the information that the different values captured at each pixel represent
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| bshanks@112 | 230 ____________________________________
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| bshanks@112 | 231 4First, because the number of features in the reduced dataset is less than in the original dataset, the running time of
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| bshanks@112 | 232 clustering algorithms may be much less. Second, it is thought that some clustering algorithms may give better results
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| bshanks@112 | 233 on reduced data.
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| bshanks@112 | 234 5In hyperspectral imaging, the bands are adjacent, and the number of different bands is larger. For conciseness, we
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| bshanks@112 | 235 discuss only hyperspectral imaging, but our methods are also well suited to multispectral imaging with many bands.
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| bshanks@112 | 236 5
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| bshanks@112 | 237
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| bshanks@112 | 238 adjacent wavelengths of light, which can be combined to make a spectrum. Other analysis tech-
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| bshanks@112 | 239 niques ignore the interpretation of the values measured, and their relationship to each other within
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| bshanks@112 | 240 the electromagnetic spectrum, instead treating them blindly as completely separate features.
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| bshanks@112 | 241 With both hyperspectral imaging and spatial gene expression data, each location in space
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| bshanks@112 | 242 is associated with more than three numerical feature values. The analysis of hyperspectral im-
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| bshanks@112 | 243 ages can involve supervised classification and unsupervised learning. Often hyperspectral images
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| bshanks@112 | 244 come from satellites looking at the Earth, and it is desirable to classify what sort of objects occupy
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| bshanks@112 | 245 a given area of land. Sometimes detailed training data is not available, in which case it is desirable
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| bshanks@112 | 246 at least to cluster together those regions of land which contain similar objects.
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| bshanks@112 | 247 We believe that it may be possible for these two different field to share some common compu-
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| bshanks@112 | 248 tational tools. To this end, we intend to make use of existing hyperspectral imaging software when
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| bshanks@112 | 249 possible, and to develop new software in such a way so as to make it easy to use for the purpose
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| bshanks@112 | 250 of hyperspectral image analysis, as well as for our primary purpose of spatial gene expression
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| bshanks@112 | 251 data analysis.
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| bshanks@112 | 252 Related work
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| bshanks@112 | 253
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| bshanks@112 | 254 Figure 2: Gene Pitx2
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| bshanks@112 | 255 is selectively underex-
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| bshanks@112 | 256 pressed in area SS. As noted above, the GIS community has developed tools for supervised
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| bshanks@112 | 257 classification and unsupervised clustering in the context of the analysis
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| bshanks@120 | 258 of hyperspectral imaging data. One tool is Spectral Python[5]. Spectral
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| bshanks@112 | 259 Python implements various supervised and unsupervised classification
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| bshanks@112 | 260 methods, as well as utility functions for loading, viewing, and saving
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| bshanks@112 | 261 spatial data. Although Spectral Python has feature extraction methods
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| bshanks@112 | 262 (such as principal components analysis) which create a small set of
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| bshanks@112 | 263 new features computed based on the original features, it does not have
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| bshanks@112 | 264 feature selection methods, that is, methods to select a small subset
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| bshanks@112 | 265 out of the original features (although feature selection in hyperspectral
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| bshanks@120 | 266 imaging has been investigated by others[20].
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| bshanks@112 | 267 There is a substantial body of work on the analysis of gene expression data. Most of this con-
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| bshanks@120 | 268 cerns gene expression data which are not fundamentally spatial6. Here we review only that work
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| bshanks@112 | 269 which concerns the automated analysis of spatial gene expression data with respect to anatomy.
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| bshanks@120 | 270 Relating to Goal 1, GeneAtlas[6] and EMAGE [25] allow the user to construct a search query by
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| bshanks@112 | 271 demarcating regions and then specifying either the strength of expression or the name of another
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| bshanks@112 | 272 gene or dataset whose expression pattern is to be matched. Neither GeneAtlas nor EMAGE allow
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| bshanks@112 | 273 one to search for combinations of genes that define a region in concert.
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| bshanks@120 | 274 Relating to Goal 2, EMAGE[25] allows the user to select a dataset from among a large number
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| bshanks@112 | 275 of alternatives, or by running a search query, and then to cluster the genes within that dataset.
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| bshanks@112 | 276 EMAGE clusters via hierarchical complete linkage clustering.
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| bshanks@120 | 277 [16] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene
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| bshanks@112 | 278 Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the
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| bshanks@112 | 279 seed voxel, (2) yields a list of genes which are overexpressed in that cluster. Correlation: The user
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| bshanks@112 | 280 selects a seed voxel and the system then shows the user how much correlation there is between
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| bshanks@112 | 281 the gene expression profile of the seed voxel and every other voxel. Clusters: AGEA includes a
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| bshanks@120 | 282 preset hierarchical clustering of voxels based on a recursive bifurcation algorithm with correlation
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| bshanks@112 | 283 ____________________________________
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| bshanks@120 | 284 6By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by
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| bshanks@112 | 285 spatial coordinates; not just data which have only a few different locations or which is indexed by anatomical label.
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| bshanks@112 | 286 6
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| bshanks@112 | 287
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| bshanks@112 | 288 as the similarity metric. AGEA has been applied to the cortex. The paper describes interesting
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| bshanks@112 | 289 results on the structure of correlations between voxel gene expression profiles within a handful of
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| bshanks@112 | 290 cortical areas. However, that analysis neither looks for genes marking cortical areas, nor does it
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| bshanks@112 | 291 suggest a cortical map based on gene expression data. Neither of the other components of AGEA
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| bshanks@112 | 292 can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes for the
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| bshanks@112 | 293 cortical areas; and AGEA’s hierarchical clustering does not produce clusters corresponding to the
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| bshanks@120 | 294 cortical areas7.
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| bshanks@112 | 295
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| bshanks@112 | 296
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| bshanks@104 | 297 Figure 3: The top row shows the two
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| bshanks@104 | 298 genes which (individually) best predict
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| bshanks@104 | 299 area AUD, according to logistic regres-
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| bshanks@112 | 300 sion. The bottom row shows the two
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| bshanks@112 | 301 genes which (individually) best match
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| bshanks@112 | 302 area AUD, according to gradient sim-
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| bshanks@104 | 303 ilarity. From left to right and top to
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| bshanks@104 | 304 bottom, the genes are Ssr1, Efcbp1,
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| bshanks@120 | 305 Ptk7, and Aph1a. [7] looks at the mean expression level of genes within
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| bshanks@112 | 306 anatomical regions, and applies a Student’s t-test to de-
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| bshanks@112 | 307 termine whether the mean expression level of a gene is
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| bshanks@112 | 308 significantly higher in the target region. This relates to
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| bshanks@120 | 309 our Goal 1. [7] also clusters genes, relating to our Goal
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| bshanks@112 | 310 2. For each cluster, prototypical spatial expression pat-
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| bshanks@112 | 311 terns were created by averaging the genes in the cluster.
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| bshanks@112 | 312 The prototypes were analyzed manually, without cluster-
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| bshanks@112 | 313 ing voxels.
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| bshanks@112 | 314 These related works differ from our strategy for Goal
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| bshanks@112 | 315 1 in at least three ways. First, they find only single genes,
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| bshanks@112 | 316 whereas we will also look for combinations of genes.
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| bshanks@112 | 317 Second, they usually can only use overexpression as
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| bshanks@112 | 318 a marker, whereas we will also search for underexpres-
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| bshanks@112 | 319 sion. Third, they use scores based on pointwise expres-
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| bshanks@112 | 320 sion levels, whereas we will also use geometric scores
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| bshanks@112 | 321 such as gradient similarity (described in Preliminary Re-
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| bshanks@112 | 322 sults). Figures 4, 2, and 3 in the Preliminary Results
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| bshanks@112 | 323 section contain evidence that each of our three choices
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| bshanks@112 | 324 is the right one.
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| bshanks@120 | 325 [11] describes a technique to find combinations of
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| bshanks@112 | 326 marker genes to pick out an anatomical region. They
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| bshanks@112 | 327 use an evolutionary algorithm to evolve logical operators which combine boolean (thresholded)
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| bshanks@112 | 328 images in order to match a target image. They apply their technique for finding combinations of
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| bshanks@112 | 329 marker genes for the purpose of clustering genes around a “seed gene”.
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| bshanks@112 | 330 Relating to our Goal 2, some researchers have attempted to parcellate cortex on the basis of
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| bshanks@120 | 331 non-gene expression data. For example, [18], [2], [19], and [1] associate spots on the cortex with
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| bshanks@120 | 332 the radial profile8 of response to some stain ([13] uses MRI), extract features from this profile, and
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| bshanks@112 | 333 then use similarity between surface pixels to cluster.
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| bshanks@120 | 334 [23] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In
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| bshanks@112 | 335 addition to manual analysis, two clustering methods were employed, a modified Non-negative
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| bshanks@112 | 336 Matrix Factorization (NNMF), and a hierarchical bifurcation clustering scheme using correlation as
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| bshanks@120 | 337 similarity. The paper yielded impressive results, proving the usefulness of computational genomic
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| bshanks@112 | 338 ____________________________________
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| bshanks@120 | 339 7In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but
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| bshanks@112 | 340 the same layer are often stronger than pairwise correlations between the gene expression of voxels in different layers
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| bshanks@112 | 341 but the same area. Therefore, a pairwise voxel correlation clustering algorithm will tend to create clusters representing
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| bshanks@112 | 342 cortical layers, not areas.
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| bshanks@120 | 343 8A radial profile is a profile along a line perpendicular to the cortical surface.
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| bshanks@112 | 344 7
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| bshanks@112 | 345
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| bshanks@112 | 346 anatomy. We have run NNMF on the cortical dataset, and while the results are promising, other
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| bshanks@112 | 347 methods may perform as well or better (see Preliminary Results, Figure 6).
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| bshanks@112 | 348 Comparing previous work with our Goal 1, there has been fruitful work on finding marker genes,
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| bshanks@112 | 349 but only one of the projects explored combinations of marker genes, and none of them compared
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| bshanks@112 | 350 the results obtained by using different algorithms or scoring methods. Comparing previous work
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| bshanks@112 | 351 with Goal 2, although some projects obtained clusterings, there has not been much comparison
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| bshanks@112 | 352 between different algorithms or scoring methods, so it is likely that the best clustering method for
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| bshanks@112 | 353 this application has not yet been found. Also, none of these projects did a separate dimensionality
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| bshanks@112 | 354 reduction step before clustering pixels, or tried to cluster genes first in order to guide automated
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| bshanks@112 | 355 clustering of pixels into spatial regions, or used co-clustering algorithms.
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| bshanks@112 | 356 In summary, (a) only one of the previous projects explores combinations of marker genes, (b)
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| bshanks@112 | 357 there has been almost no comparison of different algorithms or scoring methods, and (c) there
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| bshanks@112 | 358 has been no work on computationally finding marker genes applied to cortical areas, or on finding
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| bshanks@112 | 359 a hierarchical clustering that will yield a map of cortical areas de novo from gene expression data.
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| bshanks@112 | 360 Our project is guided by a concrete application with a well-specified criterion of success (how
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| bshanks@112 | 361 well we can find marker genes for / reproduce the layout of cortical areas), which will provide a
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| bshanks@112 | 362 solid basis for comparing different methods.
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| bshanks@112 | 363 _________________________________________________
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| bshanks@112 | 364 Data sharing plan
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| bshanks@112 | 365
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| bshanks@112 | 366
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| bshanks@104 | 367 Figure 4: Upper left: wwc1. Upper
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| bshanks@104 | 368 right: mtif2. Lower left: wwc1 + mtif2
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| bshanks@104 | 369 (each pixel’s value on the lower left is
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| bshanks@104 | 370 the sum of the corresponding pixels in
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| bshanks@112 | 371 the upper row). We are enthusiastic about the sharing of methods and
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| bshanks@112 | 372 data, and at the conclusion of the project, we will make
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| bshanks@112 | 373 all of our data and computer source code publically avail-
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| bshanks@112 | 374 able, either in supplemental attachments to publications,
|
| bshanks@112 | 375 or on a website. The source code will be released under
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| bshanks@112 | 376 the GNU Public License. We intend to include a soft-
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| bshanks@112 | 377 ware program which, when run, will take as input the
|
| bshanks@112 | 378 Allen Brain Atlas raw data, and produce as output all
|
| bshanks@112 | 379 numbers and charts found in publications resulting from
|
| bshanks@112 | 380 the project. Source code to be released will include ex-
|
| bshanks@120 | 381 tensions to Caret[8], an existing open-source scientific
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| bshanks@112 | 382 imaging program, and to Spectral Python. Data to be
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| bshanks@112 | 383 released will include the 2-D “flat map” dataset. This
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| bshanks@112 | 384 dataset will be submitted to a machine learning dataset
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| bshanks@112 | 385 repository.
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| bshanks@112 | 386 Broader impacts
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| bshanks@112 | 387 In addition to validating the usefulness of the algorithms,
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| bshanks@112 | 388 the application of these methods to cortex will produce
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| bshanks@112 | 389 immediate benefits, because there are currently no known genetic markers for most cortical areas.
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| bshanks@112 | 390 The method developed in Goal 1 will be applied to each cortical area to find a set of marker
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| bshanks@112 | 391 genes such that the combinatorial expression pattern of those genes uniquely picks out the target
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| bshanks@112 | 392 area. Finding marker genes will be useful for drug discovery as well as for experimentation be-
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| bshanks@112 | 393 cause marker genes can be used to design interventions which selectively target individual cortical
|
| bshanks@112 | 394 areas.
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| bshanks@120 | 395 The application of the marker gene finding algorithm to the cortex will also support the develop-
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| bshanks@112 | 396 8
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| bshanks@112 | 397
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| bshanks@112 | 398 ment of new neuroanatomical methods. In addition to finding markers for each individual cortical
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| bshanks@112 | 399 areas, we will find a small panel of genes that can find many of the areal boundaries at once.
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| bshanks@112 | 400 The method developed in Goal 2 will provide a genoarchitectonic viewpoint that will contribute
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| bshanks@112 | 401 to the creation of a better cortical map.
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| bshanks@112 | 402 The methods we will develop will be applicable to other datasets beyond the brain, and even to
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| bshanks@112 | 403 datasets outside of biology. The software we develop will be useful for the analysis of hyperspectral
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| bshanks@112 | 404 images. Our project will draw attention to this area of overlap between neuroscience and GIS, and
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| bshanks@112 | 405 may lead to future collaborations between these two fields. The cortical dataset that we produce
|
| bshanks@112 | 406 will be useful in the machine learning community as a sample dataset that new algorithms can be
|
| bshanks@112 | 407 tested against. The availability of this sample dataset to the machine learning community may lead
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| bshanks@112 | 408 to more interest in the design of machine learning algorithms to analyze spatial gene expression.
|
| bshanks@112 | 409 _
|
| bshanks@112 | 410 Preliminary Results
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| bshanks@112 | 411 Format conversion between SEV, MATLAB, NIFTI
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| bshanks@120 | 412 We have created software to (politely) download all of the SEV files9 from the Allen Institute web-
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| bshanks@120 | 413 site. We have also created software to convert between the SEV, MATLAB, and NIFTI file formats,
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| bshanks@120 | 414 as well as some of Caret’s file formats.
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| bshanks@112 | 415 Flatmap of cortex
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| bshanks@112 | 416 We downloaded the ABA data and selected only those voxels which belong to cerebral cortex.
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| bshanks@120 | 417 We divided the cortex into hemispheres. Using Caret[8], we created a mesh representation of the
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| bshanks@112 | 418 surface of the selected voxels. For each gene, and for each node of the mesh, we calculated an
|
| bshanks@112 | 419 average of the gene expression of the voxels “underneath” that mesh node. We then flattened
|
| bshanks@112 | 420 the cortex, creating a two-dimensional mesh. We converted this grid into a MATLAB matrix. We
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| bshanks@112 | 421 manually traced the boundaries of each of 46 cortical areas from the ABA coronal reference atlas
|
| bshanks@112 | 422 slides, and converted this region data into MATLAB format.
|
| bshanks@112 | 423 At this point, the data are in the form of a number of 2-D matrices, all in registration, with the
|
| bshanks@112 | 424 matrix entries representing a grid of points (pixels) over the cortical surface. There is one 2-D
|
| bshanks@112 | 425 matrix whose entries represent the regional label associated with each surface pixel. And for each
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| bshanks@112 | 426 gene, there is a 2-D matrix whose entries represent the average expression level underneath each
|
| bshanks@112 | 427 surface pixel. The features and the target area are both functions on the surface pixels. They can
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| bshanks@112 | 428 be referred to as scalar fields over the space of surface pixels; alternately, they can be thought of
|
| bshanks@112 | 429 as images which can be displayed on the flatmapped surface.
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| bshanks@112 | 430 Feature selection and scoring methods
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| bshanks@112 | 431 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes
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| bshanks@112 | 432 serve as a marker. For example, see Figure 2.
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| bshanks@112 | 433 Correlation Recall that the instances are surface pixels, and consider the problem of attempt-
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| bshanks@112 | 434 ing to classify each instance as either a member of a particular anatomical area, or not. The target
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| bshanks@112 | 435 area can be represented as a boolean mask over the surface pixels.
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| bshanks@120 | 436 We calculated the correlation between each gene and each cortical area. The top row of Figure
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| bshanks@120 | 437 1 shows the three genes most correlated with area SS.
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| bshanks@120 | 438 9SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.
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| bshanks@112 | 439 9
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| bshanks@112 | 440
|
| bshanks@112 | 441 Conditional entropy
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| bshanks@112 | 442 For each region, we created and ran a forward stepwise procedure which attempted to find
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| bshanks@112 | 443 pairs of genes such that the conditional entropy of the target area’s boolean mask, conditioned
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| bshanks@112 | 444 upon the gene pair’s thresholded expression levels, is minimized.
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| bshanks@112 | 445 This finds pairs of genes which are most informative (at least at these threshold levels) relative
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| bshanks@112 | 446 to the question, “Is this surface pixel a member of the target area?”. The advantage over linear
|
| bshanks@112 | 447 methods such as logistic regression is that this takes account of arbitrarily nonlinear relationships;
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| bshanks@112 | 448 for example, if the XOR of two variables predicts the target, conditional entropy would notice,
|
| bshanks@112 | 449 whereas linear methods would not.
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| bshanks@112 | 450 Gradient similarity We noticed that the previous two scoring methods, which are pointwise,
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| bshanks@112 | 451 often found genes whose pattern of expression did not look similar in shape to the target region.
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| bshanks@112 | 452 For this reason we designed a non-pointwise scoring method to detect when a gene had a pattern
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| bshanks@112 | 453 of expression which looked like it had a boundary whose shape is similar to the shape of the target
|
| bshanks@112 | 454 region. We call this scoring method “gradient similarity”. The formula is:
|
| bshanks@112 | 455 ∑
|
| bshanks@112 | 456 pixel<img src="cmsy8-32.png" alt="∈" />pixels cos(∠∇1 -∠∇2) ⋅|∇1| + |∇2|
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| bshanks@112 | 457 2 ⋅ pixel_value1 + pixel_value2
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| bshanks@112 | 458 2
|
| bshanks@112 | 459 where ∇1 and ∇2 are the gradient vectors of the two images at the current pixel; ∠∇i is the
|
| bshanks@112 | 460 angle of the gradient of image i at the current pixel; |∇i| is the magnitude of the gradient of image
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| bshanks@112 | 461 i at the current pixel; and pixel_valuei is the value of the current pixel in image i.
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| bshanks@112 | 462 The intuition is that we want to see if the borders of the pattern in the two images are similar; if
|
| bshanks@112 | 463 the borders are similar, then both images will have corresponding pixels with large gradients (be-
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| bshanks@112 | 464 cause this is a border) which are oriented in a similar direction (because the borders are similar).
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| bshanks@112 | 465 Gradient similarity provides information complementary to correlation
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| bshanks@112 | 466 To show that gradient similarity can provide useful information that cannot be detected via
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| bshanks@112 | 467 pointwise analyses, consider Fig. 3. The pointwise method in the top row identifies genes which
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| bshanks@112 | 468 express more strongly in AUD than outside of it; its weakness is that this includes many areas
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| bshanks@112 | 469 which don’t have a salient border matching the areal border. The geometric method identifies
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| bshanks@112 | 470 genes whose salient expression border seems to partially line up with the border of AUD; its
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| bshanks@112 | 471 weakness is that this includes genes which don’t express over the entire area.
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| bshanks@112 | 472 Areas which can be identified by single genes Using gradient similarity, we have already
|
| bshanks@112 | 473 found single genes which roughly identify some areas and groupings of areas. For each of these
|
| bshanks@112 | 474 areas, an example of a gene which roughly identifies it is shown in Figure 5. We have not yet
|
| bshanks@112 | 475 cross-verified these genes in other atlases.
|
| bshanks@112 | 476 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT
|
| bshanks@112 | 477 (anterior part of cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal),
|
| bshanks@112 | 478 ACAv (ventral anterior cingulate), VIS (visual), AUD (auditory).
|
| bshanks@112 | 479 These results validate our expectation that the ABA dataset can be exploited to find marker
|
| bshanks@112 | 480 genes for many cortical areas, while also validating the relevancy of our new scoring method,
|
| bshanks@112 | 481 gradient similarity.
|
| bshanks@112 | 482 10
|
| bshanks@112 | 483
|
| bshanks@112 | 484
|
| bshanks@112 | 485
|
| bshanks@112 | 486
|
| bshanks@112 | 487
|
| bshanks@104 | 488 Figure 5: From left to right and top
|
| bshanks@104 | 489 to bottom, single genes which roughly
|
| bshanks@104 | 490 identify areas SS (somatosensory pri-
|
| bshanks@112 | 491 mary + supplemental), SSs (supple-
|
| bshanks@104 | 492 mental somatosensory), PIR (piriform),
|
| bshanks@112 | 493 FRP (frontal pole), RSP (retrosplenial),
|
| bshanks@112 | 494 COApm (Cortical amygdalar, poste-
|
| bshanks@112 | 495 rior part, medial zone). Grouping
|
| bshanks@112 | 496 some areas together, we have also
|
| bshanks@112 | 497 found genes to identify the groups
|
| bshanks@104 | 498 ACA+PL+ILA+DP+ORB+MO (anterior
|
| bshanks@104 | 499 cingulate, prelimbic, infralimbic, dor-
|
| bshanks@104 | 500 sal peduncular, orbital, motor), poste-
|
| bshanks@112 | 501 rior and lateral visual (VISpm, VISpl,
|
| bshanks@104 | 502 VISI, VISp; posteromedial, posterolat-
|
| bshanks@112 | 503 eral, lateral, and primary visual; the
|
| bshanks@104 | 504 posterior and lateral visual area is dis-
|
| bshanks@104 | 505 tinguished from its neighbors, but not
|
| bshanks@104 | 506 from the entire rest of the cortex). The
|
| bshanks@112 | 507 genes are Pitx2, Aldh1a2, Ppfibp1,
|
| bshanks@112 | 508 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. Combinations of multiple genes are useful and
|
| bshanks@112 | 509 necessary for some areas
|
| bshanks@112 | 510 In Figure 4, we give an example of a cortical area
|
| bshanks@112 | 511 which is not marked by any single gene, but which can be
|
| bshanks@112 | 512 identified combinatorially. According to logistic regres-
|
| bshanks@112 | 513 sion, gene wwc1 is the best fit single gene for predicting
|
| bshanks@112 | 514 whether or not a pixel on the cortical surface belongs to
|
| bshanks@112 | 515 the motor area (area MO). The upper-left picture in Fig-
|
| bshanks@112 | 516 ure 4 shows wwc1’s spatial expression pattern over the
|
| bshanks@112 | 517 cortex. The lower-right boundary of MO is represented
|
| bshanks@112 | 518 reasonably well by this gene, but the gene overshoots
|
| bshanks@112 | 519 the upper-left boundary. This flattened 2-D representa-
|
| bshanks@112 | 520 tion does not show it, but the area corresponding to the
|
| bshanks@112 | 521 overshoot is the medial surface of the cortex. MO is only
|
| bshanks@112 | 522 found on the dorsal surface. Gene mtif2 is shown in the
|
| bshanks@112 | 523 upper-right. Mtif2 captures MO’s upper-left boundary, but
|
| bshanks@112 | 524 not its lower-right boundary. Mtif2 does not express very
|
| bshanks@112 | 525 much on the medial surface. By adding together the val-
|
| bshanks@112 | 526 ues at each pixel in these two figures, we get the lower-
|
| bshanks@112 | 527 left image. This combination captures area MO much
|
| bshanks@112 | 528 better than any single gene.
|
| bshanks@112 | 529 This shows that our proposal to develop a method to
|
| bshanks@112 | 530 find combinations of marker genes is both possible and
|
| bshanks@112 | 531 necessary.
|
| bshanks@112 | 532 Multivariate supervised learning
|
| bshanks@112 | 533 Forward stepwise logistic regression Logistic regres-
|
| bshanks@112 | 534 sion is a popular method for predictive modeling of cat-
|
| bshanks@112 | 535 egorical data. As a pilot run, for five cortical areas (SS,
|
| bshanks@112 | 536 AUD, RSP, VIS, and MO), we performed forward step-
|
| bshanks@112 | 537 wise logistic regression to find single genes, pairs of
|
| bshanks@112 | 538 genes, and triplets of genes which predict areal identify.
|
| bshanks@112 | 539 This is an example of feature selection integrated with
|
| bshanks@112 | 540 prediction using a stepwise wrapper. Some of the sin-
|
| bshanks@112 | 541 gle genes found were shown in various figures through-
|
| bshanks@112 | 542 out this document, and Figure 4 shows a combination of
|
| bshanks@112 | 543 genes which was found.
|
| bshanks@112 | 544 SVM on all genes at once
|
| bshanks@112 | 545 In order to see how well one can do when looking at
|
| bshanks@112 | 546 all genes at once, we ran a support vector machine to
|
| bshanks@112 | 547 classify cortical surface pixels based on their gene ex-
|
| bshanks@112 | 548 pression profiles. We achieved classification accuracy of
|
| bshanks@120 | 549 about 81%10. However, as noted above, a classifier that
|
| bshanks@112 | 550 ____________________________________
|
| bshanks@120 | 551 105-fold cross-validation.
|
| bshanks@112 | 552 11
|
| bshanks@112 | 553
|
| bshanks@112 | 554 looks at all the genes at once isn’t as practically useful
|
| bshanks@112 | 555 as a classifier that uses only a few genes.
|
| bshanks@112 | 556 Data-driven redrawing of the cortical map
|
| bshanks@112 | 557 We have applied the following dimensionality reduction algorithms to reduce the dimensionality
|
| bshanks@112 | 558 of the gene expression profile associated with each pixel: Principal Components Analysis (PCA),
|
| bshanks@112 | 559 Simple PCA, Multi-Dimensional Scaling, Isomap, Landmark Isomap, Laplacian eigenmaps, Local
|
| bshanks@112 | 560 Tangent Space Alignment, Stochastic Proximity Embedding, Fast Maximum Variance Unfolding,
|
| bshanks@112 | 561 Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing many of
|
| bshanks@112 | 562 the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the first, second,
|
| bshanks@112 | 563 and third rows of Figure 6.
|
| bshanks@112 | 564 After applying the dimensionality reduction, we ran clustering algorithms on the reduced data.
|
| bshanks@112 | 565 To date we have tried k-means and spectral clustering. The results of k-means after PCA, NNMF,
|
| bshanks@112 | 566 and landmark Isomap are shown in the bottom row of Figure 6. To compare, the leftmost picture
|
| bshanks@112 | 567 on the bottom row of Figure 6 shows some of the major subdivisions of cortex. These results show
|
| bshanks@112 | 568 that different dimensionality reduction techniques capture different aspects of the data and lead
|
| bshanks@112 | 569 to different clusterings, indicating the utility of our proposal to produce a detailed comparison of
|
| bshanks@112 | 570 these techniques as applied to the domain of genomic anatomy.
|
| bshanks@112 | 571 Many areas are captured by clusters of genes We also clustered the genes using gradient
|
| bshanks@112 | 572 similarity to see if the spatial regions defined by any clusters matched known anatomical regions.
|
| bshanks@112 | 573 Figure 7 shows, for ten sample gene clusters, each cluster’s average expression pattern, com-
|
| bshanks@112 | 574 pared to a known anatomical boundary. This suggests that it is worth attempting to cluster genes,
|
| bshanks@112 | 575 and then to use the results to cluster pixels.
|
| bshanks@112 | 576 Our plan: what remains to be done
|
| bshanks@112 | 577 Flatmap cortex and segment cortical layers
|
| bshanks@112 | 578 There are multiple ways to flatten 3-D data into 2-D. We will compare mappings from manifolds to
|
| bshanks@120 | 579 planes which attempt to preserve size (such as the one used by Caret[8]) with mappings which
|
| bshanks@112 | 580 preserve angle (conformal maps). We will also develop a segmentation algorithm to automatically
|
| bshanks@112 | 581 identify the layer boundaries.
|
| bshanks@112 | 582 Develop algorithms that find genetic markers for anatomical regions
|
| bshanks@112 | 583 Scoring measures and feature selection We will develop scoring methods for evaluating how
|
| bshanks@112 | 584 good individual genes are at marking areas. We will compare pointwise, geometric, and information-
|
| bshanks@112 | 585 theoretic measures. We already developed one entirely new scoring method (gradient similarity),
|
| bshanks@112 | 586 but we may develop more. Scoring measures that we will explore will include the L1 norm, cor-
|
| bshanks@112 | 587 relation, expression energy ratio, conditional entropy, gradient similarity, Jaccard similarity, Dice
|
| bshanks@112 | 588 similarity, Hough transform, and statistical tests such as Student’s t-test, and the Mann-Whitney
|
| bshanks@112 | 589 U test (a non-parametric test). In addition, any classifier induces a scoring measure on genes by
|
| bshanks@112 | 590 taking the prediction error when using that gene to predict the target.
|
| bshanks@112 | 591 Using some combination of these measures, we will develop a procedure to find single marker
|
| bshanks@112 | 592 genes for anatomical regions: for each cortical area, we will rank the genes by their ability to
|
| bshanks@112 | 593 delineate that area. We will quantitatively compare the list of single genes generated by our
|
| bshanks@112 | 594 method to the lists generated by methods which are mentioned in Related Work.
|
| bshanks@112 | 595 12
|
| bshanks@112 | 596
|
| bshanks@112 | 597
|
| bshanks@104 | 598 Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec-
|
| bshanks@112 | 599 ond row: the first 6 reduced dimensions, using NNMF. Third row: the
|
| bshanks@112 | 600 first six reduced dimensions, using landmark Isomap. Bottom row:
|
| bshanks@112 | 601 examples of kmeans clustering applied to reduced datasets to find
|
| bshanks@112 | 602 7 clusters. Left: 19 of the major subdivisions of the cortex. Sec-
|
| bshanks@112 | 603 ond from left: PCA. Third from left: NNMF. Right: Landmark Isomap.
|
| bshanks@112 | 604 Additional details: In the third and fourth rows, 7 dimensions were
|
| bshanks@112 | 605 found, but only 6 displayed. In the last row: for PCA, 50 dimensions
|
| bshanks@112 | 606 were used; for NNMF, 6 dimensions were used; for landmark Isomap,
|
| bshanks@112 | 607 7 dimensions were used. Some cortical areas have
|
| bshanks@112 | 608 no single marker genes but
|
| bshanks@112 | 609 can be identified by com-
|
| bshanks@112 | 610 binatorial coding. This re-
|
| bshanks@112 | 611 quires multivariate scoring
|
| bshanks@112 | 612 measures and feature se-
|
| bshanks@112 | 613 lection procedures. Many
|
| bshanks@112 | 614 of the measures, such
|
| bshanks@112 | 615 as expression energy, gra-
|
| bshanks@112 | 616 dient similarity, Jaccard,
|
| bshanks@112 | 617 Dice, Hough, Student’s t,
|
| bshanks@112 | 618 and Mann-Whitney U are
|
| bshanks@112 | 619 univariate. We will ex-
|
| bshanks@112 | 620 tend these scoring mea-
|
| bshanks@112 | 621 sures for use in multivariate
|
| bshanks@112 | 622 feature selection, that is,
|
| bshanks@112 | 623 for scoring how well com-
|
| bshanks@112 | 624 binations of genes, rather
|
| bshanks@112 | 625 than individual genes, can
|
| bshanks@112 | 626 distinguish a target area.
|
| bshanks@112 | 627 There are existing mul-
|
| bshanks@112 | 628 tivariate forms of some
|
| bshanks@112 | 629 of the univariate scoring
|
| bshanks@112 | 630 measures, for example,
|
| bshanks@112 | 631 Hotelling’s T-square is a
|
| bshanks@112 | 632 multivariate analog of Stu-
|
| bshanks@112 | 633 dent’s t.
|
| bshanks@112 | 634 We will develop a fea-
|
| bshanks@112 | 635 ture selection procedure for choosing the best small set of marker genes for a given anatomical
|
| bshanks@112 | 636 area. In addition to using the scoring measures that we develop, we will also explore (a) feature
|
| bshanks@112 | 637 selection using a stepwise wrapper over “vanilla” classifiers such as logistic regression, (b) super-
|
| bshanks@112 | 638 vised learning methods such as decision trees which incrementally/greedily combine single gene
|
| bshanks@112 | 639 markers into sets, and (c) supervised learning methods which use soft constraints to minimize
|
| bshanks@112 | 640 number of features used, such as sparse support vector machines (SVMs).
|
| bshanks@112 | 641 Since errors of displacement and of shape may cause genes and target areas to match less
|
| bshanks@112 | 642 than they should, we will consider the robustness of feature selection methods in the presence of
|
| bshanks@112 | 643 error. Some of these methods, such as the Hough transform, are designed to be resistant in the
|
| bshanks@112 | 644 presence of error, but many are not.
|
| bshanks@112 | 645 An area may be difficult to identify because the boundaries are misdrawn in the atlas, or be-
|
| bshanks@112 | 646 cause the shape of the natural domain of gene expression corresponding to the area is different
|
| bshanks@112 | 647 from the shape of the area as recognized by anatomists. We will develop extensions to our pro-
|
| bshanks@120 | 648 cedure which (a) detect when a difficult area could be fit if its boundary were redrawn slightly11,
|
| bshanks@112 | 649 ____________________________________
|
| bshanks@120 | 650 11Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene ex-
|
| bshanks@112 | 651 pression by multiple sources of evidence. Interestingly, the need to detect “natural spatial domains of gene expression”
|
| bshanks@112 | 652 in a data-driven fashion means that the methods of Goal 2 might be useful in achieving Goal 1, as well – particularly
|
| bshanks@112 | 653 13
|
| bshanks@112 | 654
|
| bshanks@112 | 655 and (b) detect when a difficult area could be combined with adjacent areas to create a larger area
|
| bshanks@112 | 656 which can be fit.
|
| bshanks@112 | 657 A future publication on the method that we develop in Goal 1 will review the scoring measures
|
| bshanks@112 | 658 and quantitatively compare their performance in order to provide a foundation for future research
|
| bshanks@112 | 659 of methods of marker gene finding. We will measure the robustness of the scoring measures as
|
| bshanks@112 | 660 well as their absolute performance on our dataset.
|
| bshanks@112 | 661 Develop algorithms to suggest a division of a structure into anatomical parts
|
| bshanks@112 | 662
|
| bshanks@112 | 663 Figure 7: Prototypes corresponding to sample gene clus-
|
| bshanks@112 | 664 ters, clustered by gradient similarity. Region boundaries for
|
| bshanks@112 | 665 the region that most matches each prototype are overlaid. Dimensionality reduction on gene
|
| bshanks@112 | 666 expression profiles We have al-
|
| bshanks@112 | 667 ready described the application of
|
| bshanks@112 | 668 ten dimensionality reduction algo-
|
| bshanks@112 | 669 rithms for the purpose of replacing
|
| bshanks@112 | 670 the gene expression profiles, which
|
| bshanks@112 | 671 are vectors of about 4000 gene ex-
|
| bshanks@112 | 672 pression levels, with a smaller num-
|
| bshanks@112 | 673 ber of features. We plan to further ex-
|
| bshanks@112 | 674 plore and interpret these results, as
|
| bshanks@112 | 675 well as to apply other unsupervised
|
| bshanks@112 | 676 learning algorithms, including inde-
|
| bshanks@112 | 677 pendent components analysis, self-
|
| bshanks@112 | 678 organizing maps, and generative models such as deep Boltzmann machines. We will explore
|
| bshanks@112 | 679 ways to quantitatively compare the relevance of the different dimensionality reduction methods for
|
| bshanks@112 | 680 identifying cortical areal boundaries.
|
| bshanks@112 | 681 Dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene
|
| bshanks@112 | 682 expression profiles, the same techniques can be applied instead to the pixels. It is possible that
|
| bshanks@112 | 683 the features generated in this way by some dimensionality reduction techniques will directly corre-
|
| bshanks@112 | 684 spond to interesting spatial regions.
|
| bshanks@112 | 685 Clustering and segmentation on pixels We will explore clustering and image segmentation
|
| bshanks@112 | 686 algorithms in order to segment the pixels into regions. We will explore k-means, spectral cluster-
|
| bshanks@120 | 687 ing, gene shaving[10], recursive division clustering, multivariate generalizations of edge detectors,
|
| bshanks@112 | 688 multivariate generalizations of watershed transformations, region growing, active contours, graph
|
| bshanks@112 | 689 partitioning methods, and recursive agglomerative clustering with various linkage functions. These
|
| bshanks@112 | 690 methods can be combined with dimensionality reduction.
|
| bshanks@112 | 691 Clustering on genes We have already shown that the procedure of clustering genes according
|
| bshanks@112 | 692 to gradient similarity, and then creating an averaged prototype of each cluster’s expression pattern,
|
| bshanks@112 | 693 yields some spatial patterns which match cortical areas (Figure 7). We will further explore the
|
| bshanks@112 | 694 clustering of genes.
|
| bshanks@112 | 695 In addition to using the cluster expression prototypes directly to identify spatial regions, this
|
| bshanks@112 | 696 might be useful as a component of dimensionality reduction. For example, one could imagine
|
| bshanks@112 | 697 clustering similar genes and then replacing their expression levels with a single average expression
|
| bshanks@112 | 698 ____________________________________
|
| bshanks@112 | 699 discriminative dimensionality reduction.
|
| bshanks@112 | 700 14
|
| bshanks@112 | 701
|
| bshanks@112 | 702 level, thereby removing some redundancy from the gene expression profiles. One could then
|
| bshanks@112 | 703 perform clustering on pixels (possibly after a second dimensionality reduction step) in order to
|
| bshanks@112 | 704 identify spatial regions. It remains to be seen whether removal of redundancy would help or hurt
|
| bshanks@112 | 705 the ultimate goal of identifying interesting spatial regions.
|
| bshanks@112 | 706 Co-clustering We will explore some algorithms which simultaneously incorporate clustering
|
| bshanks@120 | 707 on instances and on features (in our case, pixels and genes), for example, IRM[12]. These are
|
| bshanks@112 | 708 called co-clustering or biclustering algorithms.
|
| bshanks@112 | 709 Compare different methods In order to tell which method is best for genomic anatomy, for
|
| bshanks@112 | 710 each experimental method we will compare the cortical map found by unsupervised learning to a
|
| bshanks@112 | 711 cortical map derived from the Allen Reference Atlas. We will explore various quantitative metrics
|
| bshanks@112 | 712 that purport to measure how similar two clusterings are, such as Jaccard, Rand index, Fowlkes-
|
| bshanks@112 | 713 Mallows, variation of information, Larsen, Van Dongen, and others.
|
| bshanks@112 | 714 Discriminative dimensionality reduction In addition to using a purely data-driven approach
|
| bshanks@112 | 715 to identify spatial regions, it might be useful to see how well the known regions can be recon-
|
| bshanks@112 | 716 structed from a small number of features, even if those features are chosen by using knowledge of
|
| bshanks@112 | 717 the regions. For example, linear discriminant analysis could be used as a dimensionality reduction
|
| bshanks@112 | 718 technique in order to identify a few features which are the best linear summary of gene expression
|
| bshanks@112 | 719 profiles for the purpose of discriminating between regions. This reduced feature set could then be
|
| bshanks@112 | 720 used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the reference
|
| bshanks@112 | 721 atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is.
|
| bshanks@112 | 722 Apply the new methods to the cortex
|
| bshanks@112 | 723 Using the methods developed in Goal 1, we will present, for each cortical area, a short list of
|
| bshanks@112 | 724 markers to identify that area; and we will also present lists of “panels” of genes that can be used
|
| bshanks@112 | 725 to delineate many areas at once.
|
| bshanks@112 | 726 Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible
|
| bshanks@112 | 727 for an unrelated combination of genes to seem to identify an area when in fact it is only coinci-
|
| bshanks@112 | 728 dence. There are three ways we will validate our marker genes to guard against this. First, we
|
| bshanks@112 | 729 will confirm that putative combinations of marker genes express the same pattern in both hemi-
|
| bshanks@112 | 730 spheres. Second, we will manually validate our final results on other gene expression datasets
|
| bshanks@120 | 731 such as EMAGE, GeneAtlas, and GENSAT[9]. Third, we may conduct ISH experiments jointly with
|
| bshanks@112 | 732 collaborators to get further data on genes of particular interest.
|
| bshanks@112 | 733 Using the methods developed in Goal 2, we will present one or more hierarchical cortical
|
| bshanks@112 | 734 maps. We will identify and explain how the statistical structure in the gene expression data led to
|
| bshanks@112 | 735 any unexpected or interesting features of these maps, and we will provide biological hypotheses
|
| bshanks@112 | 736 to interpret any new cortical areas, or groupings of areas, which are discovered.
|
| bshanks@112 | 737 Apply the new methods to hyperspectral datasets
|
| bshanks@112 | 738 Our software will be able to read and write file formats common in the hyperspectral imaging
|
| bshanks@112 | 739 community such as Erdas LAN and ENVI, and it will be able to convert between the SEV and NIFTI
|
| bshanks@112 | 740 formats from neuroscience and the ENVI format from GIS. The methods developed in Goals 1 and
|
| bshanks@112 | 741 2 will be implemented either as part of Spectral Python or as a separate tool that interoperates
|
| bshanks@112 | 742 with Spectral Python. The methods will be run on hyperspectral satellite image datasets, and their
|
| bshanks@112 | 743 performance will be compared to existing hyperspectral analysis techniques.
|
| bshanks@112 | 744 15
|
| bshanks@112 | 745
|
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| bshanks@112 | 862 mitzakis, Colin Dewey, Nicholas J Dickens, Mark Diekhans, Sheila Dodge, Inna Dubchak,
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| bshanks@112 | 863 Diane M Dunn, Sean R Eddy, Laura Elnitski, Richard D Emes, Pallavi Eswara, Eduardo
|
| bshanks@112 | 864 Eyras, Adam Felsenfeld, Ginger A Fewell, Paul Flicek, Karen Foley, Wayne N Frankel, Lu-
|
| bshanks@112 | 865 cinda A Fulton, Robert S Fulton, Terrence S Furey, Diane Gage, Richard A Gibbs, Gustavo
|
| bshanks@112 | 866 Glusman, Sante Gnerre, Nick Goldman, Leo Goodstadt, Darren Grafham, Tina A Graves,
|
| bshanks@112 | 867 Eric D Green, Simon Gregory, Roderic Guig, Mark Guyer, Ross C Hardison, David Haussler,
|
| bshanks@120 | 868 18
|
| bshanks@120 | 869
|
| bshanks@112 | 870 Yoshihide Hayashizaki, LaDeana W Hillier, Angela Hinrichs, Wratko Hlavina, Timothy Holzer,
|
| bshanks@112 | 871 Fan Hsu, Axin Hua, Tim Hubbard, Adrienne Hunt, Ian Jackson, David B Jaffe, L Steven John-
|
| bshanks@112 | 872 son, Matthew Jones, Thomas A Jones, Ann Joy, Michael Kamal, Elinor K Karlsson, Donna
|
| bshanks@112 | 873 Karolchik, Arkadiusz Kasprzyk, Jun Kawai, Evan Keibler, Cristyn Kells, W James Kent, An-
|
| bshanks@112 | 874 drew Kirby, Diana L Kolbe, Ian Korf, Raju S Kucherlapati, Edward J Kulbokas, David Kulp,
|
| bshanks@112 | 875 Tom Landers, J P Leger, Steven Leonard, Ivica Letunic, Rosie Levine, Jia Li, Ming Li, Chris-
|
| bshanks@112 | 876 tine Lloyd, Susan Lucas, Bin Ma, Donna R Maglott, Elaine R Mardis, Lucy Matthews, Evan
|
| bshanks@112 | 877 Mauceli, John H Mayer, Megan McCarthy, W Richard McCombie, Stuart McLaren, Kirsten
|
| bshanks@112 | 878 McLay, John D McPherson, Jim Meldrim, Beverley Meredith, Jill P Mesirov, Webb Miller, Tra-
|
| bshanks@112 | 879 cie L Miner, Emmanuel Mongin, Kate T Montgomery, Michael Morgan, Richard Mott, James C
|
| bshanks@112 | 880 Mullikin, Donna M Muzny, William E Nash, Joanne O Nelson, Michael N Nhan, Robert Nicol,
|
| bshanks@112 | 881 Zemin Ning, Chad Nusbaum, Michael J O’Connor, Yasushi Okazaki, Karen Oliver, Emma
|
| bshanks@112 | 882 Overton-Larty, Lior Pachter, Gens Parra, Kymberlie H Pepin, Jane Peterson, Pavel Pevzner,
|
| bshanks@112 | 883 Robert Plumb, Craig S Pohl, Alex Poliakov, Tracy C Ponce, Chris P Ponting, Simon Potter,
|
| bshanks@112 | 884 Michael Quail, Alexandre Reymond, Bruce A Roe, Krishna M Roskin, Edward M Rubin, Alis-
|
| bshanks@112 | 885 tair G Rust, Ralph Santos, Victor Sapojnikov, Brian Schultz, Jrg Schultz, Matthias S Schwartz,
|
| bshanks@112 | 886 Scott Schwartz, Carol Scott, Steven Seaman, Steve Searle, Ted Sharpe, Andrew Sheridan,
|
| bshanks@112 | 887 Ratna Shownkeen, Sarah Sims, Jonathan B Singer, Guy Slater, Arian Smit, Douglas R Smith,
|
| bshanks@112 | 888 Brian Spencer, Arne Stabenau, Nicole Stange-Thomann, Charles Sugnet, Mikita Suyama,
|
| bshanks@112 | 889 Glenn Tesler, Johanna Thompson, David Torrents, Evanne Trevaskis, John Tromp, Cather-
|
| bshanks@112 | 890 ine Ucla, Abel Ureta-Vidal, Jade P Vinson, Andrew C Von Niederhausern, Claire M Wade,
|
| bshanks@112 | 891 Melanie Wall, Ryan J Weber, Robert B Weiss, Michael C Wendl, Anthony P West, Kris
|
| bshanks@112 | 892 Wetterstrand, Raymond Wheeler, Simon Whelan, Jamey Wierzbowski, David Willey, Sophie
|
| bshanks@112 | 893 Williams, Richard K Wilson, Eitan Winter, Kim C Worley, Dudley Wyman, Shan Yang, Shiaw-
|
| bshanks@112 | 894 Pyng Yang, Evgeny M Zdobnov, Michael C Zody, and Eric S Lander. Initial sequencing and
|
| bshanks@112 | 895 comparative analysis of the mouse genome. Nature, 420(6915):520–62, December 2002.
|
| bshanks@112 | 896 PMID: 12466850.
|
| bshanks@112 | 897 19
|
| bshanks@112 | 898
|
| bshanks@112 | 899
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