cg

annotate grant.html @ 0:29eee29f9bc1

initial commit to hg version control repository
author bshanks@bshanks-salk.dyndns.org
date Sat Apr 11 19:12:32 2009 -0700 (16 years ago)
parents
children 7487ad7f5d8f

rev   line source
bshanks@0 1 Specific aims
bshanks@0 2 Massive new datasets obtained with techniques such as in situ hybridization
bshanks@0 3 (ISH) and BAC-transgenics allow the expression levels of many genes at many
bshanks@0 4 locations to be compared. Our goal is to develop automated methods to relate
bshanks@0 5 spatial variation in gene expression to anatomy. We want to find marker genes
bshanks@0 6 for specific anatomical regions, and also to draw new anatomical maps based on
bshanks@0 7 gene expression patterns. We have three specific aims:
bshanks@0 8 (1) develop an algorithm to screen spatial gene expression data for combina-
bshanks@0 9 tions of marker genes which selectively target anatomical regions
bshanks@0 10 (2) develop an algorithm to suggest new ways of carving up a structure into
bshanks@0 11 anatomical subregions, based on spatial patterns in gene expression
bshanks@0 12 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains
bshanks@0 13 a flattened version of the Allen Mouse Brain Atlas ISH data, as well as
bshanks@0 14 the boundaries of cortical anatomical areas. Use this dataset to validate
bshanks@0 15 the methods developed in (1) and (2).
bshanks@0 16 In addition to validating the usefulness of the algorithms, the application of
bshanks@0 17 these methods to cerebral cortex will produce immediate benefits, because there
bshanks@0 18 are currently no known genetic markers for many cortical areas. The results
bshanks@0 19 of the project will support the development of new ways to selectively target
bshanks@0 20 cortical areas, and it will support the development of a method for identifying
bshanks@0 21 the cortical areal boundaries present in small tissue samples.
bshanks@0 22 All algorithms that we develop will be implemented in an open-source soft-
bshanks@0 23 ware toolkit. The toolkit, as well as the machine-readable datasets developed
bshanks@0 24 in aim (3), will be published and freely available for others to use.
bshanks@0 25 Background and significance
bshanks@0 26 Aim 1
bshanks@0 27 Machine learning terminology
bshanks@0 28 The task of looking for marker genes for anatomical subregions means that one
bshanks@0 29 is looking for a set of genes such that, if the expression level of those genes is
bshanks@0 30 known, then the locations of the subregions can be inferred.
bshanks@0 31 If we define the subregions so that they cover the entire anatomical structure
bshanks@0 32 to be divided, then instead of saying that we are using gene expression to find
bshanks@0 33 the locations of the subregions, we may say that we are using gene expression to
bshanks@0 34 determine to which subregion each voxel within the structure belongs. We call
bshanks@0 35 this a classification task, because each voxel is being assigned to a class (namely,
bshanks@0 36 its subregion).
bshanks@0 37 Therefore, an understanding of the relationship between the combination of
bshanks@0 38 their expression levels and the locations of the subregions may be expressed as
bshanks@0 39 1
bshanks@0 40
bshanks@0 41 a function. The input to this function is a voxel, along with the gene expression
bshanks@0 42 levels within that voxel; the output is the subregional identity of the target
bshanks@0 43 voxel, that is, the subregion to which the target voxel belongs. We call this
bshanks@0 44 function a classifier. In general, the input to a classifier is called an instance,
bshanks@0 45 and the output is called a label.
bshanks@0 46 The object of aim 1 is not to produce a single classifier, but rather to develop
bshanks@0 47 an automated method for determining a classifier for any known anatomical
bshanks@0 48 structure. Therefore, we seek a procedure by which a gene expression dataset
bshanks@0 49 may be analyzed in concert with an anatomical atlas in order to produce a
bshanks@0 50 classifier. Such a procedure is a type of a machine learning procedure. The
bshanks@0 51 construction of the classifier is called training (also learning), and the initial
bshanks@0 52 gene expression dataset used in the construction of the classifier is called training
bshanks@0 53 data.
bshanks@0 54 In the machine learning literature, this sort of procedure may be thought
bshanks@0 55 of as a supervised learning task, defined as a task in whcih the goal is to learn
bshanks@0 56 a mapping from instances to labels, and the training data consists of a set of
bshanks@0 57 instances (voxels) for which the labels (subregions) are known.
bshanks@0 58 Each gene expression level is called a feature, and the selection of which
bshanks@0 59 genes to include is called feature selection. Feature selection is one component
bshanks@0 60 of the task of learning a classifier. Some methods for learning classifiers start
bshanks@0 61 out with a separate feature selection phase, whereas other methods combine
bshanks@0 62 feature selection with other aspects of training.
bshanks@0 63 One class of feature selection methods assigns some sort of score to each
bshanks@0 64 candidate gene. The top-ranked genes are then chosen. Some scoring measures
bshanks@0 65 can assign a score to a set of selected genes, not just to a single gene; in this
bshanks@0 66 case, a dynamic procedure may be used in which features are added and sub-
bshanks@0 67 tracted from the selected set depending on how much they raise the score. Such
bshanks@0 68 procedures are called “stepwise” or “greedy”.
bshanks@0 69 Although the classifier itself may only look at the gene expression data within
bshanks@0 70 each voxel before classifying that voxel, the learning algorithm which constructs
bshanks@0 71 the classifier may look over the entire dataset. We can categorize score-based
bshanks@0 72 feature selection methods depending on how the score of calculated. Often
bshanks@0 73 the score calculation consists of assigning a sub-score to each voxel, and then
bshanks@0 74 aggregating these sub-scores into a final score (the aggregation is often a sum or
bshanks@0 75 a sum of squares). If only information from nearby voxels is used to calculate a
bshanks@0 76 voxel’s sub-score, then we say it is a local scoring method. If only information
bshanks@0 77 from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a
bshanks@0 78 pointwise scoring method.
bshanks@0 79 Key questions when choosing a learning method are: What are the instances?
bshanks@0 80 What are the features? How are the features chosen? Here are four principles
bshanks@0 81 that outline our answers to these questions.
bshanks@0 82 Principle 1: Combinatorial gene expression
bshanks@0 83 Above, we defined an “instance” as the combination of a voxel with the “asso-
bshanks@0 84 ciated gene expression data”. In our case this refers to the expression level of
bshanks@0 85 2
bshanks@0 86
bshanks@0 87 genes within the voxel, but should we include the expression levels of all genes,
bshanks@0 88 or only a few of them?
bshanks@0 89 It is too much to hope that every anatomical region of interest will be iden-
bshanks@0 90 tified by a single gene. For example, in the cortex, there are some areas which
bshanks@0 91 are not clearly delineated by any gene included in the Allen Brain Atlas (ABA)
bshanks@0 92 dataset. However, at least some of these areas can be delineated by looking
bshanks@0 93 at combinations of genes (an example of an area for which multiple genes are
bshanks@0 94 necessary and sufficient is provided in Preliminary Results).
bshanks@0 95 Principle 2: Only look at combinations of small numbers of genes
bshanks@0 96 When the classifier classifies a voxel, it is only allowed to look at the expression of
bshanks@0 97 the genes which have been selected as features. The more data that is available
bshanks@0 98 to a classifier, the better that it can do. For example, perhaps there are weak
bshanks@0 99 correlations over many genes that add up to a strong signal. So, why not include
bshanks@0 100 every gene as a feature? The reason is that we wish to employ the classifier in
bshanks@0 101 situations in which it is not feasible to gather data about every gene. For
bshanks@0 102 example, if we want to use the expression of marker genes as a trigger for some
bshanks@0 103 regionally-targeted intervention, then our intervention must contain a molecular
bshanks@0 104 mechanism to check the expression level of each marker gene before it triggers.
bshanks@0 105 It is currently infeasible to design a molecular trigger that checks the level of
bshanks@0 106 more than a handful of genes. Similarly, if the goal is to develop a procedure to
bshanks@0 107 do ISH on tissue samples in order to label their anatomy, then it is infeasible
bshanks@0 108 to label more than a few genes. Therefore, we must select only a few genes as
bshanks@0 109 features.
bshanks@0 110 Principle 3: Use geometry in feature selection
bshanks@0 111 When doing feature selection with score-based methods, the simplest thing to
bshanks@0 112 do would be to score the performance of each voxel by itself and then combine
bshanks@0 113 these scores; this is pointwise scoring. A more powerful approach is to also use
bshanks@0 114 information about the geometric relations between each voxel and its neighbors;
bshanks@0 115 this requires non-pointwise, local scoring methods. See Preliminary Results for
bshanks@0 116 evidence of the complementary nature of pointwise and local scoring methods.
bshanks@0 117 Principle 4: Work in 2-D whenever possible
bshanks@0 118 There are many anatomical structures which are commonly characterized in
bshanks@0 119 terms of a two-dimensional manifold. When it is known that the structure that
bshanks@0 120 one is looking for is two-dimensional, the results may be improved by allowing
bshanks@0 121 the analysis algorithm to take advantage of this prior knowledge. In addition,
bshanks@0 122 it is easier for humans to visualize and work with 2-D data.
bshanks@0 123 Therefore, when possible, the instances should represent pixels, not voxels.
bshanks@0 124 3
bshanks@0 125
bshanks@0 126 Aim 3
bshanks@0 127 Background
bshanks@0 128 The cortex is divided into areas and layers. To a first approximation, the par-
bshanks@0 129 cellation of the cortex into areas can be drawn as a 2-D map on the surface
bshanks@0 130 of the cortex. In the third dimension, the boundaries between the areas con-
bshanks@0 131 tinue downwards into the cortical depth, perpendicular to the surface. The layer
bshanks@0 132 boundaries run parallel to the surface. One can picture an area of the cortex as
bshanks@0 133 a slice of many-layered cake.
bshanks@0 134 Although it is known that different cortical areas have distinct roles in both
bshanks@0 135 normal functioning and in disease processes, there are no known marker genes
bshanks@0 136 for many cortical areas. When it is necessary to divide a tissue sample into
bshanks@0 137 cortical areas, this is a manual process that requires a skilled human to combine
bshanks@0 138 multiple visual cues and interpret them in the context of their approximate
bshanks@0 139 location upon the cortical surface.
bshanks@0 140 Even the questions of how many areas should be recognized in cortex, and
bshanks@0 141 what their arrangement is, are still not completely settled. A proposed division
bshanks@0 142 of the cortex into areas is called a cortical map. In the rodent, the lack of a
bshanks@0 143 single agreed-upon map can be seen by contrasting the recent maps given by
bshanks@0 144 Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While
bshanks@0 145 the maps are certainly very similar in their general arrangement, significant
bshanks@0 146 differences remain in the details.
bshanks@0 147 Significance
bshanks@0 148 The method developed in aim (1) will be applied to each cortical area to find
bshanks@0 149 a set of marker genes such that the combinatorial expression pattern of those
bshanks@0 150 genes uniquely picks out the target area. Finding marker genes will be useful
bshanks@0 151 for drug discovery as well as for experimentation because marker genes can be
bshanks@0 152 used to design interventions which selectively target individual cortical areas.
bshanks@0 153 The application of the marker gene finding algorithm to the cortex will
bshanks@0 154 also support the development of new neuroanatomical methods. In addition to
bshanks@0 155 finding markers for each individual cortical areas, we will find a small panel
bshanks@0 156 of genes that can find many of the areal boundaries at once. This panel of
bshanks@0 157 marker genes will allow the development of an ISH protocol that will allow
bshanks@0 158 experimenters to more easily identify which anatomical areas are present in
bshanks@0 159 small samples of cortex.
bshanks@0 160 The method developed in aim (3) will provide a genoarchitectonic viewpoint
bshanks@0 161 that will contribute to the creation of a better map. The development of present-
bshanks@0 162 day cortical maps was driven by the application of histological stains. It is
bshanks@0 163 conceivable that if a different set of stains had been available which identified
bshanks@0 164 a different set of features, then the today’s cortical maps would have come out
bshanks@0 165 differently. Since the number of classes of stains is small compared to the number
bshanks@0 166 of genes, it is likely that there are many repeated, salient spatial patterns in
bshanks@0 167 the gene expression which have not yet been captured by any stain. Therefore,
bshanks@0 168 4
bshanks@0 169
bshanks@0 170 current ideas about cortical anatomy need to incorporate what we can learn
bshanks@0 171 from looking at the patterns of gene expression.
bshanks@0 172 While we do not here propose to analyze human gene expression data, it is
bshanks@0 173 conceivable that the methods we propose to develop could be used to suggest
bshanks@0 174 modifications to the human cortical map as well.
bshanks@0 175 Related work
bshanks@0 176 Preliminary work
bshanks@0 177 Justification of principles 1 thur 3
bshanks@0 178 Principle 1: Combinatorial gene expression
bshanks@0 179 Here we give an example of a cortical area which is not marked by any single
bshanks@0 180 gene, but which can be identified combinatorially. according to logistic regres-
bshanks@0 181 sion, gene wwc11 is the best fit single gene for predicting whether or not a pixel
bshanks@0 182 on the cortical surface belongs to the motor area (area MO). The upper-left
bshanks@0 183 picture in Figure shows wwc1’s spatial expression pattern over the cortex. The
bshanks@0 184 lower-right boundary of MO is represented reasonably well by this gene, however
bshanks@0 185 the gene overshoots the upper-left boundary. This flattened 2-D representation
bshanks@0 186 does not show it, but the area corresponding to the overshoot is the medial
bshanks@0 187 surface of the cortex. MO is only found on the lateral surface (todo).
bshanks@0 188 Gnee mtif22 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s
bshanks@0 189 upper-left boundary, but not its lower-right boundary. Mtif2 does not express
bshanks@0 190 very much on the medial surface. By adding together the values at each pixel
bshanks@0 191 in these two figures, we get the lower-left of Figure . This combination captures
bshanks@0 192 area MO much better than any single gene.
bshanks@0 193 Principle 2: Only look at combinations of small numbers of genes
bshanks@0 194 In order to see how well one can do when looking at all genes at once, we ran
bshanks@0 195 a support vector machine to classify cortical surface pixels based on their gene
bshanks@0 196 expression profiles. We achieved classification accuracy of about 81%3. As noted
bshanks@0 197 above, however, a classifier that looks at all the genes at once isn’t practically
bshanks@0 198 useful.
bshanks@0 199 The requirement to find combinations of only a small number of genes limits
bshanks@0 200 us from straightforwardly applying many of the most simple techniques from
bshanks@0 201 the field of supervised machine learning. In the parlance of machine learning,
bshanks@0 202 our task combines feature selection with supervised learning.
bshanks@0 203 __________________________
bshanks@0 204 1“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
bshanks@0 205 2“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
bshanks@0 206 3Using the Shogun SVM package (todo:cite), with parameters type=GMNPSVM (multi-
bshanks@0 207 class b-SVM), kernal = gaussian with sigma = 0.1, c = 10, epsilon = 1e-1 – these are the
bshanks@0 208 first parameters we tried, so presumably performance would improve with different choices of
bshanks@0 209 parameters. 5-fold cross-validation.
bshanks@0 210 5
bshanks@0 211
bshanks@0 212
bshanks@0 213
bshanks@0 214 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2
bshanks@0 215 (each pixel’s value on the lower left is the sum of the corresponding pixels in
bshanks@0 216 the upper row). Within each picture, the vertical axis roughly corresponds to
bshanks@0 217 anterior at the top and posterior at the bottom, and the horizontal axis roughly
bshanks@0 218 corresponds to medial at the left and lateral at the right. The red outline is
bshanks@0 219 the boundary of region MO. Pixels are colored approximately according to the
bshanks@0 220 density of expressing cells underneath each pixel, with red meaning a lot of
bshanks@0 221 expression and blue meaning little.
bshanks@0 222 6
bshanks@0 223
bshanks@0 224
bshanks@0 225
bshanks@0 226 Figure 2: The top row shows the three genes which (individually) best predict
bshanks@0 227 area AUD, according to logistic regression. The bottom row shows the three
bshanks@0 228 genes which (individually) best match area AUD, according to gradient similar-
bshanks@0 229 ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a,
bshanks@0 230 Ptk7, Aph1a again, and Lepr
bshanks@0 231 Principle 3: Use geometry
bshanks@0 232 To show that local geometry can provide useful information that cannot be
bshanks@0 233 detected via pointwise analyses, consider Fig. . The top row of Fig. displays
bshanks@0 234 the 3 genes which most match area AUD, according to a pointwise method4. The
bshanks@0 235 bottom row displays the 3 genes which most match AUD according to a method
bshanks@0 236 which considers local geometry5 The pointwise method in the top row identifies
bshanks@0 237 genes which express more strongly in AUD than outside of it; its weakness is that
bshanks@0 238 this includes many areas which don’t have a salient border matching the areal
bshanks@0 239 border. The geometric method identifies genes whose salient expression border
bshanks@0 240 seems to partially line up with the border of AUD; its weakness is that this
bshanks@0 241 includes genes which don’t express over the entire area. Genes which have high
bshanks@0 242 rankings using both pointwise and border criteria, such as Aph1a in the example,
bshanks@0 243 may be particularly good markers. None of these genes are, individually, a
bshanks@0 244 perfect marker for AUD; we deliberately chose a “difficult” area in order to
bshanks@0 245 better contrast pointwise with geometric methods.
bshanks@0 246 __________________________
bshanks@0 247 4For each gene, a logistic regression in which the response variable was whether or not a
bshanks@0 248 surface pixel was within area AUD, and the predictor variable was the value of the expression
bshanks@0 249 of the gene underneath that pixel. The resulting scores were used to rank the genes in terms
bshanks@0 250 of how well they predict area AUD.
bshanks@0 251 5For each gene the gradient similarity (see section ??) between (a) a map of the expression
bshanks@0 252 of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this
bshanks@0 253 was used to rank the genes.
bshanks@0 254 7
bshanks@0 255
bshanks@0 256 Principle 4: Work in 2-D whenever possible
bshanks@0 257 In anatomy, the manifold of interest is usually either defined by a combination
bshanks@0 258 of two relevant anatomical axes (todo), or by the surface of the structure (as is
bshanks@0 259 the case with the cortex). In the former case, the manifold of interest is a plane,
bshanks@0 260 but in the latter case it is curved. If the manifold is curved, there are various
bshanks@0 261 methods for mapping the manifold into a plane.
bshanks@0 262 The method that we will develop will begin by mapping the data into a
bshanks@0 263 2-D plane. Although the manifold that characterized cortical areas is known
bshanks@0 264 to be the cortical surface, it remains to be seen which method of mapping the
bshanks@0 265 manifold into a plane is optimal for this application. We will compare mappings
bshanks@0 266 which attempt to preserve size (such as the one used by Caret??) with mappings
bshanks@0 267 which preserve angle (conformal maps).
bshanks@0 268 Although there is much 2-D organization in anatomy, there are also struc-
bshanks@0 269 tures whose shape is fundamentally 3-dimensional. If possible, we would like
bshanks@0 270 the method we develop to include a statistical test that warns the user if the
bshanks@0 271 assumption of 2-D structure seems to be wrong.
bshanks@0 272 ——
bshanks@0 273 Massive new datasets obtained with techniques such as in situ hybridization
bshanks@0 274 (ISH) and BAC-transgenics allow the expression levels of many genes at many
bshanks@0 275 locations to be compared. This can be used to find marker genes for specific
bshanks@0 276 anatomical structures, as well as to draw new anatomical maps. Our goal is
bshanks@0 277 to develop automated methods to relate spatial variation in gene expression to
bshanks@0 278 anatomy. We have five specific aims:
bshanks@0 279 (1) develop an algorithm to screen spatial gene expression data for combi-
bshanks@0 280 nations of marker genes which selectively target individual anatomical
bshanks@0 281 structures
bshanks@0 282 (2) develop an algorithm to screen spatial gene expression data for combina-
bshanks@0 283 tions of marker genes which can be used to delineate most of the bound-
bshanks@0 284 aries between a number of anatomical structures at once
bshanks@0 285 (3) develop an algorithm to suggest new ways of dividing a structure up into
bshanks@0 286 anatomical subregions, based on spatial patterns in gene expression
bshanks@0 287 (4) create a flat (2-D) map of the mouse cerebral cortex that contains a flat-
bshanks@0 288 tened version of the Allen Mouse Brain Atlas ISH dataset, as well as the
bshanks@0 289 boundaries of anatomical areas within the cortex. For each cortical layer,
bshanks@0 290 a layer-specific flat dataset will be created. A single combined flat dataset
bshanks@0 291 will be created which averages information from all of the layers. These
bshanks@0 292 datasets will be made available in both MATLAB and Caret formats.
bshanks@0 293 (5) validate the methods developed in (1), (2) and (3) by applying them to
bshanks@0 294 the cerebral cortex datasets created in (4)
bshanks@0 295 All algorithms that we develop will be implemented in an open-source soft-
bshanks@0 296 ware toolkit. The toolkit, as well as the machine-readable datasets developed in
bshanks@0 297 8
bshanks@0 298
bshanks@0 299 aim (4) and any other intermediate dataset we produce, will be published and
bshanks@0 300 freely available for others to use.
bshanks@0 301 In addition to developing generally useful methods, the application of these
bshanks@0 302 methods to cerebral cortex will produce immediate benefits that are only one
bshanks@0 303 step removed from clinical application, while also supporting the development
bshanks@0 304 of new neuroanatomical techniques. The method developed in aim (1) will be
bshanks@0 305 applied to each cortical area to find a set of marker genes. Currently, despite
bshanks@0 306 the distinct roles of different cortical areas in both normal functioning and
bshanks@0 307 disease processes, there are no known marker genes for many cortical areas.
bshanks@0 308 Finding marker genes will be immediately useful for drug discovery as well as for
bshanks@0 309 experimentation because once marker genes for an area are known, interventions
bshanks@0 310 can be designed which selectively target that area.
bshanks@0 311 The method developed in aim (2) will be used to find a small panel of genes
bshanks@0 312 that can find most of the boundaries between areas in the cortex. Today, finding
bshanks@0 313 cortical areal boundaries in a tissue sample is a manual process that requires a
bshanks@0 314 skilled human to combine multiple visual cues over a large area of the cortical
bshanks@0 315 surface. A panel of marker genes will allow the development of an ISH protocol
bshanks@0 316 that will allow experimenters to more easily identify which anatomical areas are
bshanks@0 317 present in small samples of cortex.
bshanks@0 318 For each cortical layer, a layer-specific flat dataset will be created. A single
bshanks@0 319 combined flat dataset will be created which averages information from all of
bshanks@0 320 the layers. These datasets will be made available in both MATLAB and Caret
bshanks@0 321 formats.
bshanks@0 322 —-
bshanks@0 323 New techniques allow the expression levels of many genes at many locations
bshanks@0 324 to be compared. It is thought that even neighboring anatomical structures have
bshanks@0 325 different gene expression profiles. We propose to develop automated methods
bshanks@0 326 to relate the spatial variation in gene expression to anatomy. We will develop
bshanks@0 327 two kinds of techniques:
bshanks@0 328 (a) techniques to screen for combinations of marker genes which selectively
bshanks@0 329 target anatomical structures
bshanks@0 330 (b) techniques to suggest new ways of dividing a structure up into anatomical
bshanks@0 331 subregions, based on the shapes of contours in the gene expression
bshanks@0 332 The first kind of technique will be helpful for finding marker genes associated
bshanks@0 333 with known anatomical features. The second kind of technique will be helpful in
bshanks@0 334 creating new anatomical maps, maps which reflect differences in gene expression
bshanks@0 335 the same way that existing maps reflect differences in histology.
bshanks@0 336 We intend to develop our techniques using the adult mouse cerebral cortex
bshanks@0 337 as a testbed. The Allen Brain Atlas has collected a dataset containing the
bshanks@0 338 expression level of about 4000 genes* over a set of over 150000 voxels, with a
bshanks@0 339 spatial resolution of approximately 200 microns[?].
bshanks@0 340 We expect to discover sets of marker genes that pick out specific cortical
bshanks@0 341 areas. This will allow the development of drugs and other interventions that
bshanks@0 342 selectively target individual cortical areas. Therefore our research will lead
bshanks@0 343 9
bshanks@0 344
bshanks@0 345 to application in drug discovery, in the development of other targeted clinical
bshanks@0 346 interventions, and in the development of new experimental techniques.
bshanks@0 347 The best way to divide up rodent cortex into areas has not been completely
bshanks@0 348 determined, as can be seen by the differences in the recent maps given by Swan-
bshanks@0 349 son on the one hand, and Paxinos and Franklin on the other. It is likely that our
bshanks@0 350 study, by showing which areal divisions naturally follow from gene expression
bshanks@0 351 data, as opposed to traditional histological data, will contribute to the creation
bshanks@0 352 of a better map. While we do not here propose to analyze human gene expres-
bshanks@0 353 sion data, it is conceivable that the methods we propose to develop could be
bshanks@0 354 used to suggest modifications to the human cortical map as well.
bshanks@0 355 In the following, we will only be talking about coronal data.
bshanks@0 356 The Allen Brain Atlas provides “Smoothed Energy Volumes”, which are
bshanks@0 357 One type of artifact in the Allen Brain Atlas data is what we call a “slice
bshanks@0 358 artifact”. We have noticed two types of slice artifacts in the dataset. The first
bshanks@0 359 type, a “missing slice artifact”, occurs when the ISH procedure on a slice did
bshanks@0 360 not come out well. In this case, the Allen Brain investigators excluded the slice
bshanks@0 361 at issue from the dataset. This means that no gene expression information is
bshanks@0 362 available for that gene for the region of space covered by that slice. This results
bshanks@0 363 in an expression level of zero being assigned to voxels covered by the slice. This
bshanks@0 364 is partially but not completely ameliorated by the smoothing that is applied to
bshanks@0 365 create the Smoothed Energy Volumes. The usual end result is that a region of
bshanks@0 366 space which is shaped and oriented like a coronal slice is marked as having less
bshanks@0 367 gene expression than surrounding regions.
bshanks@0 368 The second type of slice artifact is caused by the fact that all of the slices
bshanks@0 369 have a consistent orientation. Since there may be artifacts (such as how well
bshanks@0 370 the ISH worked) which are constant within each slice but which vary between
bshanks@0 371 different slices, the result is that ceteris paribus, when one compares the genetic
bshanks@0 372 data of a voxel to another voxel within the same coronal plane, one would expect
bshanks@0 373 to find more similarity than if one compared a voxel to another voxel displaced
bshanks@0 374 along the rostrocaudal axis.
bshanks@0 375 We are enthusiastic about the sharing of methods, data, and results, and
bshanks@0 376 at the conclusion of the project, we will make all of our data and computer
bshanks@0 377 source code publically available. Our goal is that replicating our results, or
bshanks@0 378 applying the methods we develop to other targets, will be quick and easy for
bshanks@0 379 other investigators. In order to aid in understanding and replicating our results,
bshanks@0 380 we intend to include a software program which, when run, will take as input
bshanks@0 381 the Allen Brain Atlas raw data, and produce as output all numbers and charts
bshanks@0 382 found in publications resulting from the project.
bshanks@0 383 To aid in the replication of our results, we will include a script which takes
bshanks@0 384 as input the dataset in aim (3) and provides as output all of the tables in figures
bshanks@0 385 in our publications .
bshanks@0 386 We also expect to weigh in on the debate about how to best partition rodent
bshanks@0 387 cortex
bshanks@0 388 be useful for drug discovery as well
bshanks@0 389 * Another 16000 genes are available, but they do not cover the entire cerebral
bshanks@0 390 cortex with high spatial resolution.
bshanks@0 391 10
bshanks@0 392
bshanks@0 393 User-definable ROIs Combinatorial gene expression Negative as well as pos-
bshanks@0 394 itive signal Use geometry Search for local boundaries if necessary Flatmapped
bshanks@0 395 Specific aims
bshanks@0 396 Develop algorithms that find genetic markers for anatomical regions
bshanks@0 397 1. Develop scoring measures for evaluating how good individual genes are at
bshanks@0 398 marking areas: we will compare pointwise, geometric, and information-
bshanks@0 399 theoretic measures.
bshanks@0 400 2. Develop a procedure to find single marker genes for anatomical regions: for
bshanks@0 401 each cortical area, by using or combining the scoring measures developed,
bshanks@0 402 we will rank the genes by their ability to delineate each area.
bshanks@0 403 3. Extend the procedure to handle difficult areas by using combinatorial cod-
bshanks@0 404 ing: for areas that cannot be identified by any single gene, identify them
bshanks@0 405 with a handful of genes. We will consider both (a) algorithms that incre-
bshanks@0 406 mentally/greedily combine single gene markers into sets, such as forward
bshanks@0 407 stepwise regression and decision trees, and also (b) supervised learning
bshanks@0 408 techniques which use soft constraints to minimize the number of features,
bshanks@0 409 such as sparse support vector machines.
bshanks@0 410 4. Extend the procedure to handle difficult areas by combining or redrawing
bshanks@0 411 the boundaries: An area may be difficult to identify because the bound-
bshanks@0 412 aries are misdrawn, or because it does not “really” exist as a single area,
bshanks@0 413 at least on the genetic level. We will develop extensions to our procedure
bshanks@0 414 which (a) detect when a difficult area could be fit if its boundary were
bshanks@0 415 redrawn slightly, and (b) detect when a difficult area could be combined
bshanks@0 416 with adjacent areas to create a larger area which can be fit.
bshanks@0 417 Apply these algorithms to the cortex
bshanks@0 418 1. Create open source format conversion tools: we will create tools to bulk
bshanks@0 419 download the ABA dataset and to convert between SEV, NIFTI and MAT-
bshanks@0 420 LAB formats.
bshanks@0 421 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw
bshanks@0 422 the cortical area boundaries onto it.
bshanks@0 423 3. Find layer boundaries: cluster similar voxels together in order to auto-
bshanks@0 424 matically find the cortical layer boundaries.
bshanks@0 425 4. Run the procedures that we developed on the cortex: we will present, for
bshanks@0 426 each area, a short list of markers to identify that area; and we will also
bshanks@0 427 present lists of “panels” of genes that can be used to delineate many areas
bshanks@0 428 at once.
bshanks@0 429 11
bshanks@0 430
bshanks@0 431 Develop algorithms to suggest a division of a structure into anatom-
bshanks@0 432 ical parts
bshanks@0 433 1. Explore dimensionality reduction algorithms applied to pixels: including
bshanks@0 434 TODO
bshanks@0 435 2. Explore dimensionality reduction algorithms applied to genes: including
bshanks@0 436 TODO
bshanks@0 437 3. Explore clustering algorithms applied to pixels: including TODO
bshanks@0 438 4. Explore clustering algorithms applied to genes: including gene shaving,
bshanks@0 439 TODO
bshanks@0 440 5. Develop an algorithm to use dimensionality reduction and/or hierarchial
bshanks@0 441 clustering to create anatomical maps
bshanks@0 442 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic
bshanks@0 443 map of the cortex
bshanks@0 444 gradient similarity is calculated as: ∑
bshanks@0 445 pixels cos(abs(∠∇1 - ∠∇2)) ⋅|∇1|+|∇2|
bshanks@0 446 2 ⋅
bshanks@0 447 pixel_value1+pixel_value2
bshanks@0 448 2
bshanks@0 449 (todo) Technically, we say that an anatomical structure has a fundamen-
bshanks@0 450 tally 2-D organization when there exists a commonly used, generic, anatomical
bshanks@0 451 structure-preserving map from 3-D space to a 2-D manifold.
bshanks@0 452 Related work:
bshanks@0 453 The Allen Brain Institute has developed an interactive web interface called
bshanks@0 454 AGEA which allows an investigator to (1) calculate lists of genes which are se-
bshanks@0 455 lectively overexpressed in certain anatomical regions (ABA calls this the “Gene
bshanks@0 456 Finder” function) (2) to visualize the correlation between the genetic profiles of
bshanks@0 457 voxels in the dataset, and (3) to visualize a hierarchial clustering of voxels in
bshanks@0 458 the dataset [?]. AGEA is an impressive and useful tool, however, it does not
bshanks@0 459 solve the same problems that we propose to solve with this project.
bshanks@0 460 First we describe AGEA’s “Gene Finder”, and then compare it to our pro-
bshanks@0 461 posed method for finding marker genes. AGEA’s Gene Finder first asks the
bshanks@0 462 investigator to select a single “seed voxel” of interest. It then uses a clustering
bshanks@0 463 method, combined with built-in knowledge of major anatomical structures, to
bshanks@0 464 select two sets of voxels; an “ROI” and a “comparator region”*. The seed voxel
bshanks@0 465 is always contained within the ROI, and the ROI is always contained within the
bshanks@0 466 comparator region. The comparator region is similar but not identical to the
bshanks@0 467 set of voxels making up the major anatomical region containing the ROI. Gene
bshanks@0 468 Finder then looks for genes which can distinguish the ROI from the comparator
bshanks@0 469 region. Specifically, it finds genes for which the ratio (expression energy in the
bshanks@0 470 ROI) / (expression energy in the comparator region) is high.
bshanks@0 471 Informally, the Gene Finder first infers an ROI based on clustering the seed
bshanks@0 472 voxel with other voxels. Then, the Gene Finder finds genes which overexpress
bshanks@0 473 in the ROI as compared to other voxels in the major anatomical region.
bshanks@0 474 There are three major differences between our approach and Gene Finder.
bshanks@0 475 12
bshanks@0 476
bshanks@0 477 First, Gene Finder focuses on individual genes and individual ROIs in isola-
bshanks@0 478 tion. This is great for regions which can be picked out from all other regions by a
bshanks@0 479 single gene, but not all of them can (todo). There are at least two ways this can
bshanks@0 480 miss out on useful genes. First, a gene might express in part of a region, but not
bshanks@0 481 throughout the whole region, but there may be another gene which expresses
bshanks@0 482 in the rest of the region*. Second, a gene might express in a region, but not in
bshanks@0 483 any of its neighbors, but it might express also in other non-neighboring regions.
bshanks@0 484 To take advantage of these types of genes, we propose to find combinations of
bshanks@0 485 genes which, together, can identify the boundaries of all subregions within the
bshanks@0 486 containing region.
bshanks@0 487 Second, Gene Finder uses a pointwise metric, namely expression energy ratio,
bshanks@0 488 to decide whether a gene is good for picking out a region. We have found better
bshanks@0 489 results by using metrics which take into account not just single voxels, but also
bshanks@0 490 the local geometry of neighboring voxels, such as the local gradient (todo). In
bshanks@0 491 addition, we have found that often the absence of gene expression can be used
bshanks@0 492 as a marker, which will not be caught by Gene Finder’s expression energy ratio
bshanks@0 493 (todo).
bshanks@0 494 Third, Gene Finder chooses the ROI based only on the seed voxel. This
bshanks@0 495 often does not permit the user to query the ROI that they are interested in. For
bshanks@0 496 example, in all of our tests of Gene Finder in cortex, the ROIs chosen tend to
bshanks@0 497 be cortical layers, rather than cortical areas.
bshanks@0 498 In summary, when Gene Finder picks the ROI that you want, and when this
bshanks@0 499 ROI can be easily picked out from neighboring regions by single genes which
bshanks@0 500 selectively overexpress in the ROI compared to the entire major anatomical re-
bshanks@0 501 gion, Gene Finder will work. However, Gene Finder will not pick cortical areas
bshanks@0 502 as ROIs, and even if it could, many cortical areas cannot be uniquely picked out
bshanks@0 503 by the overexpression of any single gene. By contrast, we will target cortical
bshanks@0 504 areas, we will explore a variety of metrics which can complement the shortcom-
bshanks@0 505 ings of expression energy ratio, and we will use the combinatorial expression of
bshanks@0 506 genes to pick out cortical areas even when no individual gene will do.
bshanks@0 507 * The terms “ROI” and “comparator region” are our own; the ABI calls
bshanks@0 508 them the “local region” and the “larger anatomical context”. The ABI uses the
bshanks@0 509 term “specificity comparator” to mean the major anatomic region containing
bshanks@0 510 the ROI, which is not exactly identical to the comparator region.
bshanks@0 511 ** In this case, the union of the area of expression of the two genes would
bshanks@0 512 suffice; one could also imagine that there could be situations in which the in-
bshanks@0 513 tersection of multiple genes would be needed, or a combination of unions and
bshanks@0 514 intersections.
bshanks@0 515 Now we describe AGEA’s hierarchial clustering, and compare it to our pro-
bshanks@0 516 posal. The goal of AGEA’s hierarchial clustering is to generate a binary tree of
bshanks@0 517 clusters, where a cluster is a collection of voxels. AGEA begins by computing
bshanks@0 518 the Pearson correlation between each pair of voxels. They then employ a recur-
bshanks@0 519 sive divisive (top-down) hierarchial clustering procedure on the voxels, which
bshanks@0 520 means that they start with all of the voxels, and then they divide them into clus-
bshanks@0 521 ters, and then within each cluster, they divide that cluster into smaller clusters,
bshanks@0 522 etc***. At each step, the collection of voxels is partitioned into two smaller
bshanks@0 523 13
bshanks@0 524
bshanks@0 525 clusters in a way that maximizes the following quantity: average correlation
bshanks@0 526 between all possible pairs of voxels containing one voxel from each cluster.
bshanks@0 527 There are three major differences between our approach and AGEA’s hier-
bshanks@0 528 archial clustering. First, AGEA’s clustering method separates cortical layers
bshanks@0 529 before it separates cortical areas.
bshanks@0 530 following procedure is used for the purpose of dividing a collection of voxels
bshanks@0 531 into smaller clusters: partition the voxels into two sets, such that the following
bshanks@0 532 quantity is maximized:
bshanks@0 533 *** depending on which level of the tree is being created, the voxels are
bshanks@0 534 subsampled in order to save time
bshanks@0 535 does not allow the user to input anything other than a seed voxel; this means
bshanks@0 536 that for each seed voxel, there is only one
bshanks@0 537 The role of the “local region” is to serve as a region of interest for which
bshanks@0 538 marker genes are desired; the role of the “larger anatomical context” is to be
bshanks@0 539 the structure
bshanks@0 540 There are two kinds of differences between AGEA and our project; differ-
bshanks@0 541 ences that relate to the treatment of the cortex, and differences in the type of
bshanks@0 542 generalizable methods being developed. As relates
bshanks@0 543 indicate an ROI
bshanks@0 544 explore simple correlation-based relationships between voxels, genes, and
bshanks@0 545 clusters of voxels.
bshanks@0 546 There have not yet been any studies which describe the results of applying
bshanks@0 547 AGEA to the cerebral cortex; however, we suspect that the AGEA metrics are
bshanks@0 548 not optimal for the task of relating genes to cortical areas. A voxel’s gene
bshanks@0 549 expression profile depends upon both its cortical area and its cortical layer,
bshanks@0 550 however, AGEA has no mechanism to distinguish these two. As a result, voxels
bshanks@0 551 in the same layer but different areas are often clustered together by AGEA. As
bshanks@0 552 part of the project, we will compare the performance of our techniques against
bshanks@0 553 AGEA’s.
bshanks@0 554 —
bshanks@0 555 The Allen Brain Institute has developed interactive tools called AGEA which
bshanks@0 556 allow an investigator to explore simple correlation-based relationships between
bshanks@0 557 voxels, genes, and clusters of voxels. There have not yet been any studies
bshanks@0 558 which describe the results of applying AGEA to the cerebral cortex; however,
bshanks@0 559 we suspect that the AGEA metrics are not optimal for the task of relating
bshanks@0 560 genes to cortical areas. A voxel’s gene expression profile depends upon both
bshanks@0 561 its cortical area and its cortical layer, however, AGEA has no mechanism to
bshanks@0 562 distinguish these two. As a result, voxels in the same layer but different areas
bshanks@0 563 are often clustered together by AGEA. As part of the project, we will compare
bshanks@0 564 the performance of our techniques against AGEA’s.
bshanks@0 565 Another difference between our techniques and AGEA’s is that AGEA allows
bshanks@0 566 the user to enter only a voxel location, and then to either explore the rest of
bshanks@0 567 the brain’s relationship to that particular voxel, or explore a partitioning of
bshanks@0 568 the brain based on pairwise voxel correlation. If the user is interested not in a
bshanks@0 569 single voxel, but rather an entire anatomical structure, AGEA will only succeed
bshanks@0 570 to the extent that the selected voxel is a typical representative of the structure.
bshanks@0 571 14
bshanks@0 572
bshanks@0 573 As discussed in the previous paragraph, this poses problems for structures like
bshanks@0 574 cortical areas, which (because of their division into cortical layers) do not have
bshanks@0 575 a single “typical representative”.
bshanks@0 576 By contrast, in our system, the user will start by selecting, not a single voxel,
bshanks@0 577 but rather, an anatomical superstructure to be divided into pieces (for example,
bshanks@0 578 the cerebral cortex). We expect that our methods will take into account not
bshanks@0 579 just pairwise statistics between voxels, but also large-scale geometric features
bshanks@0 580 (for example, the rapidity of change in gene expression as regional boundaries
bshanks@0 581 are crossed) which optimize the discriminability of regions within the selected
bshanks@0 582 superstructure.
bshanks@0 583 —–
bshanks@0 584 screen for combinations of marker genes which selectively target anatom-
bshanks@0 585 ical structures pick delineate the boundaries between neighboring anatomical
bshanks@0 586 structures. (b) techniques to screen for marker genes which pick out anatomical
bshanks@0 587 structures of interest
bshanks@0 588 , techniques which: (a) screen for marker genes , and (b) suggest new
bshanks@0 589 anatomical maps based on
bshanks@0 590 whose expression partitions the region of interest into its anatomical sub-
bshanks@0 591 structures, and (b) use the natural contours of gene expression to suggest new
bshanks@0 592 ways of dividing an organ into
bshanks@0 593 The Allen Brain Atlas
bshanks@0 594 –
bshanks@0 595 to: brooksl@mail.nih.gov
bshanks@0 596 Hi, I’m writing to confirm the applicability of a potential research project to
bshanks@0 597 the challenge grant topic ”New computational and statistical methods for the
bshanks@0 598 analysis of large data sets from next-generation sequencing technologies”.
bshanks@0 599 We want to develop methods for the analysis of gene expression datasets that
bshanks@0 600 can be used to uncover the relationships between gene expression and anatomical
bshanks@0 601 regions. Specifically, we want to develop techniques to (a) given a set of known
bshanks@0 602 anatomical areas, identify genetic markers for each of these areas, and (b) given
bshanks@0 603 an anatomical structure whose substructure is unknown, suggest a map, that
bshanks@0 604 is, a division of the space into anatomical sub-structures, that represents the
bshanks@0 605 boundaries inherent in the gene expression data.
bshanks@0 606 We propose to develop our techniques on the Allen Brain Atlas mouse brain
bshanks@0 607 gene expression dataset by finding genetic markers for anatomical areas within
bshanks@0 608 the cerebral cortex. The Allen Brain Atlas contains a registered 3-D map of
bshanks@0 609 gene expression data with 200-micron voxel resolution which was created from
bshanks@0 610 in situ hybridization data. The dataset contains about 4000 genes which are
bshanks@0 611 available at this resolution across the entire cerebral cortex.
bshanks@0 612 Despite the distinct roles of different cortical areas in both normal function-
bshanks@0 613 ing and disease processes, there are no known marker genes for many cortical
bshanks@0 614 areas. This project will be immediately useful for both drug discovery and clini-
bshanks@0 615 cal research because once the markers are known, interventions can be designed
bshanks@0 616 which selectively target specific cortical areas.
bshanks@0 617 This techniques we develop will be useful because they will be applicable to
bshanks@0 618 the analysis of other anatomical areas, both in terms of finding marker genes
bshanks@0 619 15
bshanks@0 620
bshanks@0 621 for known areas, and in terms of suggesting new anatomical subdivisions that
bshanks@0 622 are based upon the gene expression data.
bshanks@0 623 —-
bshanks@0 624 It is likely that our study, by showing which areal divisions naturally fol-
bshanks@0 625 low from gene expression data, as opposed to traditional histological data, will
bshanks@0 626 contribute to the creation of
bshanks@0 627 there are clear genetic or chemical markers known for only a few cortical
bshanks@0 628 areas. This makes it difficult to target drugs to specific
bshanks@0 629 As part of aims (1) and (5), we will discover sets of marker genes that pick
bshanks@0 630 out specific cortical areas. This will allow the development of drugs and other
bshanks@0 631 interventions that selectively target individual cortical areas. As part of aims
bshanks@0 632 (2) and (5), we will also discover small panels of marker genes that can be used
bshanks@0 633 to delineate most of the cortical areal map.
bshanks@0 634 With aims (2) and (4), we
bshanks@0 635 There are five principals
bshanks@0 636 In addition to validating the usefulness of the algorithms, the application of
bshanks@0 637 these methods to cerebral cortex will produce immediate benefits that are only
bshanks@0 638 one step removed from clinical application.
bshanks@0 639 todo: remember to check gensat, etc for validation (mention bias/variance)
bshanks@0 640 Why it is useful to apply these methods to cortex
bshanks@0 641 There is still room for debate as to exactly how the cortex should be parcellated
bshanks@0 642 into areas.
bshanks@0 643 The best way to divide up rodent cortex into areas has not been completely
bshanks@0 644 determined,
bshanks@0 645 not yet been accounted for in
bshanks@0 646 that the expression of some genes will contain novel spatial patterns which
bshanks@0 647 are not account
bshanks@0 648 that a genoarchitectonic map
bshanks@0 649 This principle is only applicable to aim 1 (marker genes). For aim 2 (partition
bshanks@0 650 a structure in into anatomical subregions), we plan to work with many genes at
bshanks@0 651 once.
bshanks@0 652 tood: aim 2 b+s?
bshanks@0 653 Principle 5: Interoperate with existing tools
bshanks@0 654 In order for our software to be as useful as possible for our users, it will be
bshanks@0 655 able to import and export data to standard formats so that users can use our
bshanks@0 656 software in tandem with other software tools created by other teams. We will
bshanks@0 657 support the following formats: NIFTI (Neuroimaging Informatics Technology
bshanks@0 658 Initiative), SEV (Allen Brain Institute Smoothed Energy Volume), and MAT-
bshanks@0 659 LAB. This ensures that our users will not have to exclusively rely on our tools
bshanks@0 660 when analyzing data. For example, users will be able to use the data visualiza-
bshanks@0 661 tion and analysis capabilities of MATLAB and Caret alongside our software.
bshanks@0 662 16
bshanks@0 663
bshanks@0 664 To our knowledge, there is no currently available software to convert between
bshanks@0 665 these formats, so we will also provide a format conversion tool. This may be
bshanks@0 666 useful even for groups that don’t use any of our other software.
bshanks@0 667 todo: is “marker gene” even a phrase that we should use at all?
bshanks@0 668 note for aim 1 apps: combo of genes is for voxel, not within any single cell
bshanks@0 669 , as when genetic markers allow the development of selective interventions;
bshanks@0 670 the reason that one can be confident that the intervention is selective is that it
bshanks@0 671 is only turned on when a certain combination of genes is turned on and off. The
bshanks@0 672 result procedure is what assures us that when that combination is present, the
bshanks@0 673 local tissue is probably part of a certain subregion.
bshanks@0 674 The basic idea is that we want to find a procedure by
bshanks@0 675 The task of finding genes that mark anatomical areas can be phrased in
bshanks@0 676 terms of what the field of machine learning calls a “supervised learning” task.
bshanks@0 677 The goal of this task is to learn a function (the “classifier”) which
bshanks@0 678 If a person knows a combination of genes that mark an area, that implies
bshanks@0 679 that the person can be told how strong those genes express in any voxel, and
bshanks@0 680 the person can use this information to determine how
bshanks@0 681 finding how to infer the areal identity of a voxel if given the gene expression
bshanks@0 682 profile of that voxel.
bshanks@0 683 For each voxel in the cortex, we want to start with data about the gene
bshanks@0 684 expression
bshanks@0 685 There are various ways to look for marker genes. We will define some terms,
bshanks@0 686 and along the way we will describe a few design choices encountered in the
bshanks@0 687 process of creating a marker gene finding method, and then we will present four
bshanks@0 688 principles that describe which options we have chosen.
bshanks@0 689 In developing a procedure for finding marker genes, we are developing a
bshanks@0 690 procedure that takes a dataset of experimental observations and produces a
bshanks@0 691 result. One can think of the result as merely a list of genes, but really the result
bshanks@0 692 is an understanding of a predictive relationship between, on the one hand, the
bshanks@0 693 expression levels of genes, and, on the other hand, anatomical subregions.
bshanks@0 694 One way to more formally define this understanding is to look at it as a
bshanks@0 695 procedure. In this view, the result of the learning procedure is itself a procedure.
bshanks@0 696 The result procedure provides a way to use the gene expression profiles of voxels
bshanks@0 697 in a tissue sample in order to determine where the subregions are.
bshanks@0 698 This result procedure can be used directly, as when an experimenter has
bshanks@0 699 a tissue sample and needs to know what subregions are present in it, and,
bshanks@0 700 if multiple subregions are present, where they each are. Or it can be used
bshanks@0 701 indirectly; imagine that the result procedure tells us that whenever a certain
bshanks@0 702 combination of genes are expressed, the local tissue is probably part of a certain
bshanks@0 703 subregion. This means that we can then confidentally develop an intervention
bshanks@0 704 which is triggered only when that combination of genes are expressed; and to
bshanks@0 705 the extent that the result procedure is reliable, we know that the intervention
bshanks@0 706 will only be triggered in the target subregion.
bshanks@0 707 We said that the result procedure provides “a way to use the gene expression
bshanks@0 708 profiles of voxels in a tissue sample” in order to “determine where the subregions
bshanks@0 709 are”.
bshanks@0 710 17
bshanks@0 711
bshanks@0 712 Does the result procedure get as input all of the gene expression profiles
bshanks@0 713 of each voxel in the entire tissue sample, and produce as output all of the
bshanks@0 714 subregional boundaries all at once?
bshanks@0 715 it is helpful for the classifier to look at the global “shape” of gene expression
bshanks@0 716 patterns over the whole structure, rather than just nearby voxels.
bshanks@0 717 there is some small bit of additional information that can be gleaned from
bshanks@0 718 knowing the
bshanks@0 719 Design choices for a supervised learning procedure
bshanks@0 720 After all,
bshanks@0 721 there is a small correlation between the gene expression levels from distant
bshanks@0 722 voxels and
bshanks@0 723 Depending on how we intend to use the classifier, we may want to design it
bshanks@0 724 so that
bshanks@0 725 It is possible for many things to
bshanks@0 726 The choice of which data is made part of an instance
bshanks@0 727 what we seek is a procedure
bshanks@0 728 partition the tissue sample into subregions.
bshanks@0 729 each part of the anatomical structure
bshanks@0 730 must be One way to rephrase this task is to say that, instead of searching
bshanks@0 731 for the location of the subregions, we are looking to partition the tissue sample
bshanks@0 732 into subregions.
bshanks@0 733 There are various ways to look for marker genes. We will define some terms,
bshanks@0 734 and along the way we will describe a few design choices encountered in the
bshanks@0 735 process of creating a marker gene finding method, and then we will present four
bshanks@0 736 principles that describe which options we have chosen.
bshanks@0 737 In developing a procedure for finding marker genes, we are developing a
bshanks@0 738 procedure that takes a dataset of experimental observations and produces a
bshanks@0 739 result. One can think of the result as merely a list of genes, but really the result
bshanks@0 740 is an understanding of a predictive relationship between, on the one hand, the
bshanks@0 741 expression levels of genes, and, on the other hand, anatomical subregions.
bshanks@0 742 One way to more formally define this understanding is to look at it as a
bshanks@0 743 procedure. In this view, the result of the learning procedure is itself a procedure.
bshanks@0 744 The result procedure provides a way to use the gene expression profiles of voxels
bshanks@0 745 in a tissue sample in order to determine where the subregions are.
bshanks@0 746 This result procedure can be used directly, as when an experimenter has
bshanks@0 747 a tissue sample and needs to know what subregions are present in it, and,
bshanks@0 748 if multiple subregions are present, where they each are. Or it can be used
bshanks@0 749 indirectly; imagine that the result procedure tells us that whenever a certain
bshanks@0 750 combination of genes are expressed, the local tissue is probably part of a certain
bshanks@0 751 subregion. This means that we can then confidentally develop an intervention
bshanks@0 752 which is triggered only when that combination of genes are expressed; and to
bshanks@0 753 the extent that the result procedure is reliable, we know that the intervention
bshanks@0 754 will only be triggered in the target subregion.
bshanks@0 755 18
bshanks@0 756
bshanks@0 757 We said that the result procedure provides “a way to use the gene expression
bshanks@0 758 profiles of voxels in a tissue sample” in order to “determine where the subregions
bshanks@0 759 are”.
bshanks@0 760 Does the result procedure get as input all of the gene expression profiles
bshanks@0 761 of each voxel in the entire tissue sample, and produce as output all of the
bshanks@0 762 subregional boundaries all at once?
bshanks@0 763 Or are we given one voxel at a time,
bshanks@0 764 In the jargon of the field of machine learning, the result procedure is called
bshanks@0 765 a classifier.
bshanks@0 766 The task of finding genes that mark anatomical areas can be phrased in
bshanks@0 767 terms of what the field of machine learning calls a “supervised learning” task.
bshanks@0 768 The goal of this task is to learn a function (the “classifier”) which
bshanks@0 769 If a person knows a combination of genes that mark an area, that implies
bshanks@0 770 that the person can be told how strong those genes express in any voxel, and
bshanks@0 771 the person can use this information to determine how
bshanks@0 772 finding how to infer the areal identity of a voxel if given the gene expression
bshanks@0 773 profile of that voxel.
bshanks@0 774 For each voxel in the cortex, we want to start with data about the gene
bshanks@0 775 expression
bshanks@0 776 single voxels, but rather groups of voxels, such that the groups can be placed
bshanks@0 777 in some 2-D space. We will call such instances “pixels”.
bshanks@0 778 We have been speaking as if instances necessarily correspond to single voxels.
bshanks@0 779 But it is possible for instances to be groupings of many voxels, in which case
bshanks@0 780 each grouping must be assigned the same label (that is, each voxel grouping
bshanks@0 781 must stay inside a single anatomical subregion).
bshanks@0 782 In some but not all cases, the groups are either rows or columns of voxels.
bshanks@0 783 This is the case with the cerebral cortex, in which one may assume that columns
bshanks@0 784 of voxels which run perpendicular to the cortical surface all share the same areal
bshanks@0 785 identity. In the cortex, we call such an instance a “surface pixel”, because such
bshanks@0 786 an instance represents the data associated with all voxels underneath a specific
bshanks@0 787 patch of the cortical surface.
bshanks@0 788 19
bshanks@0 789
bshanks@0 790