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author bshanks@bshanks.dyndns.org
date Wed Apr 22 06:23:09 2009 -0700 (16 years ago)
parents 3dd9a1a81c23
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1 Specific aims
2 Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in
3 situ transgenic reporter, microarray voxelation, and others, allow the expression levels of many genes at many
4 locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expres-
5 sion to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical
6 maps based on gene expression patterns. We have three specific aims:
7 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which
8 selectively target anatomical regions
9 (2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions,
10 based on spatial patterns in gene expression
11 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen
12 Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending
13 the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the
14 methods developed in (1) and (2).
15 Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that
16 the methods developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located
17 in a low-dimensional space. In particular, our method could be applied to genome-wide sequencing data derived
18 from sets of tissues and disease states.
19 In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker
20 genes, and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness
21 of the algorithms, the application of these methods to cortex will produce immediate benefits, because there
22 are currently no known genetic markers for most cortical areas. The results of the project will support the
23 development of new ways to selectively target cortical areas, and it will support the development of a method for
24 identifying the cortical areal boundaries present in small tissue samples.
25 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well
26 as the machine-readable datasets developed in aim (3), will be published and freely available for others to use.
27 The challenge topic
28 This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as
29 in situ hybridization (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others,
30 allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated
31 methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific
32 anatomical regions, and also to draw new anatomical maps based on gene expression patterns.
33 The Challenge and Potential impact
34 Each of our three aims will be discussed in turn. For each aim, we will develop a conceptual framework for
35 thinking about the task, and we will present our strategy for solving it. Next we will discuss related work. At the
36 conclusion of each section, we will summarize why our strategy is different from what has been done before. At
37 the end of this section, we will describe the potential impact.
38 Aim 1: Given a map of regions, find genes that mark the regions
40 Figure 1: Gene Pitx2
41 is selectively underex-
42 pressed in area SS. Machine learning terminology: classifiers The task of looking for marker genes for
43 known anatomical regions means that one is looking for a set of genes such that, if
44 the expression level of those genes is known, then the locations of the regions can be
45 inferred.
46 If we define the regions so that they cover the entire anatomical structure to be
47 subdivided, we may say that we are using gene expression in each voxel to assign
48 that voxel to the proper area. We call this a classification task, because each voxel
49 is being assigned to a class (namely, its region). An understanding of the relationship
50 between the combination of their expression levels and the locations of the regions may
51 be expressed as a function. The input to this function is a voxel, along with the gene
52 expression levels within that voxel; the output is the regional identity of the target voxel,
53 that is, the region to which the target voxel belongs. We call this function a classifier. In general, the input to a
54 classifier is called an instance, and the output is called a label (or a class label).
55 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for
56 determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene
57 expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. The
58 initial gene expression dataset used in the construction of the classifier is called training data. In the machine
59 learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a task in
60 which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances
61 (voxels) for which the labels (regions) are known.
62 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature
63 selection. Feature selection is one component of the task of learning a classifier. Some methods for learning
64 classifiers start out with a separate feature selection phase, whereas other methods combine feature selection
65 with other aspects of training.
66 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked
67 genes are then chosen. Some scoring measures can assign a score to a set of selected genes, not just to a
68 single gene; in this case, a dynamic procedure may be used in which features are added and subtracted from the
69 selected set depending on how much they raise the score. Such procedures are called “stepwise” or “greedy”.
70 Although the classifier itself may only look at the gene expression data within each voxel before classifying
71 that voxel, the algorithm which constructs the classifier may look over the entire dataset. We can categorize
72 score-based feature selection methods depending on how the score of calculated. Often the score calculation
73 consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the
74 aggregation is often a sum or a sum of squares or average). If only information from nearby voxels is used to
75 _________________________________________
76 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
77 calculate a voxel’s sub-score, then we say it is a local scoring method. If only information from the voxel itself is
78 used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.
79 Both gene expression data and anatomical atlases have errors, due to a variety of factors. Individual subjects
80 have idiosyncratic anatomy. Subjects may be improperly registred to the atlas. The method used to measure
81 gene expression may be noisy. The atlas may have errors. It is even possible that some areas in the anatomical
82 atlas are “wrong” in that they do not have the same shape as the natural domains of gene expression to which
83 they correspond. These sources of error can affect the displacement and the shape of both the gene expression
84 data and the anatomical target areas. Therefore, it is important to use feature selection methods which are
85 robust to these kinds of errors.
86 Our strategy for Aim 1
89 Figure 2: Top row: Genes Nfic
90 and A930001M12Rik are the most
91 correlated with area SS (somatosen-
92 sory cortex). Bottom row: Genes
93 C130038G02Rik and Cacna1i are
94 those with the best fit using logistic
95 regression. Within each picture, the
96 vertical axis roughly corresponds to
97 anterior at the top and posterior at the
98 bottom, and the horizontal axis roughly
99 corresponds to medial at the left and
100 lateral at the right. The red outline is
101 the boundary of region SS. Pixels are
102 colored according to correlation, with
103 red meaning high correlation and blue
104 meaning low. Key questions when choosing a learning method are: What are the
105 instances? What are the features? How are the features chosen?
106 Here are four principles that outline our answers to these questions.
107 Principle 1: Combinatorial gene expression
108 It is too much to hope that every anatomical region of interest will be
109 identified by a single gene. For example, in the cortex, there are some
110 areas which are not clearly delineated by any gene included in the
111 Allen Brain Atlas (ABA) dataset. However, at least some of these areas
112 can be delineated by looking at combinations of genes (an example
113 of an area for which multiple genes are necessary and sufficient is
114 provided in Preliminary Studies, Figure 4). Therefore, each instance
115 should contain multiple features (genes).
116 Principle 2: Only look at combinations of small numbers of
117 genes
118 When the classifier classifies a voxel, it is only allowed to look at
119 the expression of the genes which have been selected as features.
120 The more data that are available to a classifier, the better that it can do.
121 For example, perhaps there are weak correlations over many genes
122 that add up to a strong signal. So, why not include every gene as a
123 feature? The reason is that we wish to employ the classifier in situations
124 in which it is not feasible to gather data about every gene. For example,
125 if we want to use the expression of marker genes as a trigger for some
126 regionally-targeted intervention, then our intervention must contain a
127 molecular mechanism to check the expression level of each marker
128 gene before it triggers. It is currently infeasible to design a molecular
129 trigger that checks the level of more than a handful of genes. Similarly,
130 if the goal is to develop a procedure to do ISH on tissue samples in
131 order to label their anatomy, then it is infeasible to label more than a
132 few genes. Therefore, we must select only a few genes as features.
133 The requirement to find combinations of only a small number of genes limits us from straightforwardly ap-
134 plying many of the most simple techniques from the field of supervised machine learning. In the parlance of
135 machine learning, our task combines feature selection with supervised learning.
136 Principle 3: Use geometry in feature selection
137 When doing feature selection with score-based methods, the simplest thing to do would be to score the per-
138 formance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach
139 is to also use information about the geometric relations between each voxel and its neighbors; this requires non-
140 pointwise, local scoring methods. See Preliminary Studies, figure 3 for evidence of the complementary nature of
141 pointwise and local scoring methods.
142 Principle 4: Work in 2-D whenever possible
143 There are many anatomical structures which are commonly characterized in terms of a two-dimensional
144 manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be
145 improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for
146 humans to visualize and work with 2-D data. Therefore, when possible, the instances should represent pixels,
147 not voxels.
148 Related work
151 Figure 3: The top row shows the two
152 genes which (individually) best predict
153 area AUD, according to logistic regres-
154 sion. The bottom row shows the two
155 genes which (individually) best match
156 area AUD, according to gradient sim-
157 ilarity. From left to right and top to
158 bottom, the genes are Ssr1, Efcbp1,
159 Ptk7, and Aph1a. There is a substantial body of work on the analysis of gene expres-
160 sion data, most of this concerns gene expression data which are not
161 fundamentally spatial2.
162 As noted above, there has been much work on both supervised
163 learning and there are many available algorithms for each. However,
164 the algorithms require the scientist to provide a framework for repre-
165 senting the problem domain, and the way that this framework is set
166 up has a large impact on performance. Creating a good framework
167 can require creatively reconceptualizing the problem domain, and is
168 not merely a mechanical “fine-tuning” of numerical parameters. For
169 example, we believe that domain-specific scoring measures (such as
170 gradient similarity, which is discussed in Preliminary Studies) may be
171 necessary in order to achieve the best results in this application.
172 We are aware of six existing efforts to find marker genes using spa-
173 tial gene expression data using automated methods.
174 [13] mentions the possibility of constructing a spatial region for each
175 gene, and then, for each anatomical structure of interest, computing
176 what proportion of this structure is covered by the gene’s spatial region.
177 GeneAtlas[5] and EMAGE [26] allow the user to construct a search
178 query by demarcating regions and then specifing either the strength of
179 expression or the name of another gene or dataset whose expression
180 pattern is to be matched. Neither GeneAtlas nor EMAGE allow one to
181 search for combinations of genes that define a region in concert but not separately.
182 [15 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The
183 user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list of
184 genes which are overexpressed in that cluster. Correlation: The user selects a seed voxel and the system then
185 shows the user how much correlation there is between the gene expression profile of the seed voxel and every
186 other voxel. Clusters: will be described later
187 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with
188 Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in the
189 target region.
190 [15 ] and [6] differ from our Aim 1 in at least three ways. First, [15] and [6] find only single genes, whereas
191 we will also look for combinations of genes. Second, [15] and [6] can only use overexpression as a marker,
192 whereas we will also search for underexpression. Third, [15] and [6] use scores based on pointwise expression
193 levels, whereas we will also use geometric scores such as gradient similarity (described in Preliminary Studies).
194 Figures 4, 1, and 3 in the Preliminary Studies section contain evidence that each of our three choices is the right
195 one.
196 [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use
197 an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to
198 match a target image. Their match score is Jaccard similarity.
199 _________________________________________
200 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates;
201 not just data which have only a few different locations or which is indexed by anatomical label.
202 In summary, there has been fruitful work on finding marker genes, but only one of the previous projects
203 explores combinations of marker genes, and none of these publications compare the results obtained by using
204 different algorithms or scoring methods.
205 Aim 2: From gene expression data, discover a map of regions
208 Figure 4: Upper left: wwc1. Upper
209 right: mtif2. Lower left: wwc1 + mtif2
210 (each pixel’s value on the lower left is
211 the sum of the corresponding pixels in
212 the upper row). Machine learning terminology: clustering
213 If one is given a dataset consisting merely of instances, with no
214 class labels, then analysis of the dataset is referred to as unsupervised
215 learning in the jargon of machine learning. One thing that you can do
216 with such a dataset is to group instances together. A set of similar
217 instances is called a cluster, and the activity of finding grouping the
218 data into clusters is called clustering or cluster analysis.
219 The task of deciding how to carve up a structure into anatomical
220 regions can be put into these terms. The instances are once again
221 voxels (or pixels) along with their associated gene expression profiles.
222 We make the assumption that voxels from the same anatomical region
223 have similar gene expression profiles, at least compared to the other
224 regions. This means that clustering voxels is the same as finding po-
225 tential regions; we seek a partitioning of the voxels into regions, that is,
226 into clusters of voxels with similar gene expression.
227 It is desirable to determine not just one set of regions, but also how
228 these regions relate to each other. The outcome of clustering may be
229 a hierarchial tree of clusters, rather than a single set of clusters which
230 partition the voxels. This is called hierarchial clustering.
231 Similarity scores A crucial choice when designing a clustering method is how to measure similarity, across
232 either pairs of instances, or clusters, or both. There is much overlap between scoring methods for feature
233 selection (discussed above under Aim 1) and scoring methods for similarity.
234 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering
235 task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels
236 grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get
237 reasonable results without enforcing this constraint; however, we plan to compare these results against other
238 methods which guarantee contiguous clusters.
239 Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous
240 clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are
241 thousands of color channels (one for each gene), rather than just three3. A more crucial difference is that there
242 are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not
243 appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation
244 algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these
245 algorithms are specialized for visual images.
246 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression
247 feature vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying
248 data.
249 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion
250 in the instances. However, some clustering algorithms perform better on small numbers of features4. There are
251 techniques which “summarize” a larger number of features using a smaller number of features; these techniques
252 _________________________________________
253 3There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are
254 often used to process satellite imagery.
255 4First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering
256 algorithms may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.
257 go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique
258 yields is called the reduced feature set. Note that the features in the reduced feature set do not necessarily
259 correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels.
264 Figure 5: From left to right and top
265 to bottom, single genes which roughly
266 identify areas SS (somatosensory pri-
267 mary + supplemental), SSs (supple-
268 mental somatosensory), PIR (piriform),
269 FRP (frontal pole), RSP (retrosple-
270 nial), COApm (Cortical amygdalar, pos-
271 terior part, medial zone). Grouping
272 some areas together, we have also
273 found genes to identify the groups
274 ACA+PL+ILA+DP+ORB+MO (anterior
275 cingulate, prelimbic, infralimbic, dor-
276 sal peduncular, orbital, motor), poste-
277 rior and lateral visual (VISpm, VISpl,
278 VISI, VISp; posteromedial, posterolat-
279 eral, lateral, and primary visual; the
280 posterior and lateral visual area is dis-
281 tinguished from its neighbors, but not
282 from the entire rest of the cortex). The
283 genes are Pitx2, Aldh1a2, Ppfibp1,
284 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. Clustering genes rather than voxels Although the ultimate goal is
285 to cluster the instances (voxels or pixels), one strategy to achieve this
286 goal is to first cluster the features (genes). There are two ways that
287 clusters of genes could be used.
288 Gene clusters could be used as part of dimensionality reduction:
289 rather than have one feature for each gene, we could have one reduced
290 feature for each gene cluster.
291 Gene clusters could also be used to directly yield a clustering on
292 instances. This is because many genes have an expression pattern
293 which seems to pick out a single, spatially continguous region. This
294 suggests the following procedure: cluster together genes which pick
295 out similar regions, and then to use the more popular common regions
296 as the final clusters. In Preliminary Studies, Figure 7, we show that a
297 number of anatomically recognized cortical regions, as well as some
298 “superregions” formed by lumping together a few regions, are associ-
299 ated with gene clusters in this fashion.
300 Related work
301 Some researchers have attempted to parcellate cortex on the basis of
302 non-gene expression data. For example, [18], [2], [19], and [1] asso-
303 ciate spots on the cortex with the radial profile5 of response to some
304 stain ([12] uses MRI), extract features from this profile, and then use
305 similarity between surface pixels to cluster.
306 [23] describes an analysis of the anatomy of the hippocampus us-
307 ing the ABA dataset. In addition to manual analysis, two clustering
308 methods were employed, a modified Non-negative Matrix Factoriza-
309 tion (NNMF), and a hierarchial recursive bifurcation clustering scheme
310 based on correlation as the similarity score. The paper yielded impres-
311 sive results, proving the usefulness of computational genomic anatomy.
312 We have run NNMF on the cortical dataset
313 AGEA[15] includes a preset hierarchial clustering of voxels based
314 on a recursive bifurcation algorithm with correlation as the similarity
315 metric. EMAGE[26] allows the user to select a dataset from among a
316 large number of alternatives, or by running a search query, and then to
317 cluster the genes within that dataset. EMAGE clusters via hierarchial
318 complete linkage clustering with un-centred correlation as the similarity
319 score.
320 [6] clustered genes. For each cluster, prototypical spatial expres-
321 sion patterns were created by averaging the genes in the cluster. The
322 prototypes were analyzed manually, without clustering voxels.
323 [10] applies their technique for finding combinations of marker
324 genes for the purpose of clustering genes around a “seed gene”.
325 In summary, although these projects obtained clusterings, there has
326 not been much comparison between different algorithms or scoring
327 methods, so it is likely that the best clustering method for this appli-
328 cation has not yet been found. The projects using gene expression on cortex did not attempt to make use of
329 _________________________________________
330 5A radial profile is a profile along a line perpendicular to the cortical surface.
331 the radial profile of gene expression. Also, none of these projects did a separate dimensionality reduction step
332 before clustering pixels, none tried to cluster genes first in order to guide automated clustering of pixels into
333 spatial regions, and none used co-clustering algorithms.
334 Aim 3: apply the methods developed to the cerebral cortex
339 Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec-
340 ond row: the first 6 reduced dimensions, using NNMF. Third row:
341 the first six reduced dimensions, using landmark Isomap. Bottom
342 row: examples of kmeans clustering applied to reduced datasets
343 to find 7 clusters. Left: 19 of the major subdivisions of the cortex.
344 Second from left: PCA. Third from left: NNMF. Right: Landmark
345 Isomap. Additional details: In the third and fourth rows, 7 dimen-
346 sions were found, but only 6 displayed. In the last row: for PCA,
347 50 dimensions were used; for NNMF, 6 dimensions were used; for
348 landmark Isomap, 7 dimensions were used. Background
349 The cortex is divided into areas and lay-
350 ers. Because of the cortical columnar or-
351 ganization, the parcellation of the cortex
352 into areas can be drawn as a 2-D map on
353 the surface of the cortex. In the third di-
354 mension, the boundaries between the ar-
355 eas continue downwards into the cortical
356 depth, perpendicular to the surface. The
357 layer boundaries run parallel to the sur-
358 face. One can picture an area of the cortex
359 as a slice of a six-layered cake6.
360 It is known that different cortical areas
361 have distinct roles in both normal function-
362 ing and in disease processes, yet there are
363 no known marker genes for most cortical
364 areas. When it is necessary to divide a
365 tissue sample into cortical areas, this is a
366 manual process that requires a skilled hu-
367 man to combine multiple visual cues and
368 interpret them in the context of their ap-
369 proximate location upon the cortical sur-
370 face.
371 Even the questions of how many ar-
372 eas should be recognized in cortex, and
373 what their arrangement is, are still not com-
374 pletely settled. A proposed division of the
375 cortex into areas is called a cortical map.
376 In the rodent, the lack of a single agreed-
377 upon map can be seen by contrasting the recent maps given by Swanson[22] on the one hand, and Paxinos
378 and Franklin[17] on the other. While the maps are certainly very similar in their general arrangement, significant
379 differences remain.
380 The Allen Mouse Brain Atlas dataset
381 The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male,
382 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-
383 automatically analyzed to create a digital measurement of gene expression levels at each location in each slice.
384 Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used
385 to measure one single gene; many different mouse brains were needed in order to measure the expression of
386 many genes.
387 An automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D
388 coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are
389 67x41x58 = 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain[15].
390 Mus musculus is thought to contain about 22,000 protein-coding genes[28]. The ABA contains data on about
391 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our
392 _________________________________________
393 6Outside of isocortex, the number of layers varies.
394 dataset is derived from only the coronal subset of the ABA7.
395 The ABA is not the only large public spatial gene expression dataset. However, with the exception of the ABA,
396 GenePaint, and EMAGE, most of the other resources have not (yet) extracted the expression intensity from the
397 ISH images and registered the results into a single 3-D space.
398 Related work
399 [15 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure
400 of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort
401 of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical
402 map based on gene expression data. Neither of the other components of AGEA can be applied to cortical
403 areas; AGEA’s Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA’s hierarchial
404 clustering does not produce clusters corresponding to the cortical areas8.
405 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes,
406 (b) there has been almost no comparison of different algorithms or scoring methods, and (c) there has been no
407 work on computationally finding marker genes for cortical areas, or on finding a hierarchial clustering that will
408 yield a map of cortical areas de novo from gene expression data.
409 Our project is guided by a concrete application with a well-specified criterion of success (how well we can
410 find marker genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing
411 different methods.
412 Significance
414 Figure 7: Prototypes corresponding to sample gene
415 clusters, clustered by gradient similarity. Region bound-
416 aries for the region that most matches each prototype
417 are overlayed. The method developed in aim (1) will be applied to
418 each cortical area to find a set of marker genes such
419 that the combinatorial expression pattern of those
420 genes uniquely picks out the target area. Finding
421 marker genes will be useful for drug discovery as well
422 as for experimentation because marker genes can be
423 used to design interventions which selectively target
424 individual cortical areas.
425 The application of the marker gene finding algo-
426 rithm to the cortex will also support the development
427 of new neuroanatomical methods. In addition to find-
428 ing markers for each individual cortical areas, we will
429 find a small panel of genes that can find many of the
430 areal boundaries at once. This panel of marker genes
431 will allow the development of an ISH protocol that will allow experimenters to more easily identify which anatom-
432 ical areas are present in small samples of cortex.
433 The method developed in aim (2) will provide a genoarchitectonic viewpoint that will contribute to the creation
434 of a better map. The development of present-day cortical maps was driven by the application of histological
435 stains. If a different set of stains had been available which identified a different set of features, then today’s
436 cortical maps may have come out differently. It is likely that there are many repeated, salient spatial patterns
437 _________________________________________
438 7The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected by the Allen
439 Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked
440 non-ubiquitous expression pattern”[15].
441 8In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer
442 are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a
443 pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters
444 which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area intersection
445 clusters, further work is needed to make sense of these). The reason that Gene Finder cannot the find marker genes for cortical areas
446 is that, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found, and it creates that ROI by
447 (pairwise voxel correlation) clustering around the seed.
448 in the gene expression which have not yet been captured by any stain. Therefore, cortical anatomy needs to
449 incorporate what we can learn from looking at the patterns of gene expression.
450 While we do not here propose to analyze human gene expression data, it is conceivable that the methods
451 we propose to develop could be used to suggest modifications to the human cortical map as well. In fact, the
452 methods we will develop will be applicable to other datasets beyond the brain.
453 The approach: Preliminary Studies
454 Format conversion between SEV, MATLAB, NIFTI
455 We have created software to (politely) download all of the SEV files9 from the Allen Institute website. We have
456 also created software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s
457 file formats.
458 Flatmap of cortex
459 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex.
460 We divided the cortex into hemispheres. Using Caret[7], we created a mesh representation of the surface of the
461 selected voxels. For each gene, and for each node of the mesh, we calculated an average of the gene expression
462 of the voxels “underneath” that mesh node. We then flattened the cortex, creating a two-dimensional mesh. We
463 sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this
464 grid into a MATLAB matrix. We manually traced the boundaries of each of 49 cortical areas from the ABA coronal
465 reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the
466 mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the
467 region data into MATLAB format.
468 At this point, the data are in the form of a number of 2-D matrices, all in registration, with the matrix entries
469 representing a grid of points (pixels) over the cortical surface. There is one 2-D matrix whose entries represent
470 the regional label associated with each surface pixel. And for each gene, there is a 2-D matrix whose entries
471 represent the average expression level underneath each surface pixel. We created a normalized version of the
472 gene expression data by subtracting each gene’s mean expression level (over all surface pixels) and dividing the
473 expression level of each gene by its standard deviation. The features and the target area are both functions on
474 the surface pixels. They can be referred to as scalar fields over the space of surface pixels; alternately, they can
475 be thought of as images which can be displayed on the flatmapped surface.
476 To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix
477 for each cortical layer to represent the average expression level within that layer. Cortical layers are found at
478 different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets, we have
479 extended Caret with routines that allow the depth of the ROI for volume-to-surface projection to vary. In the
480 Research Plan, we describe how we will automatically locate the layer depths. For validation, we have manually
481 demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.
482 Feature selection and scoring methods
483 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a
484 marker. See, for example, Figure 1.
485 Correlation Recall that the instances are surface pixels, and consider the problem of attempting to classify
486 each instance as either a member of a particular anatomical area, or not. The target area can be represented
487 as a boolean mask over the surface pixels.
488 We calculated the correlation between each gene and each cortical area. The top row of Figure 2 shows the
489 three genes most correlated with area SS.
490 __
491 9SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.
492 Conditional entropy
493 Foreach region, we created and ran a forward stepwise procedure which attempted to find pairs of gene
494 expression boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned
495 upon the pair of gene expression boolean masks, is minimized.
496 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the
497 question, “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic
498 regression is that it takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables
499 predicts the target, conditional entropy would notice, whereas linear methods would not.
500 Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found
501 genes whose pattern of expression did not look similar in shape to the target region. For this reason we designed
502 a non-pointwise scoring method to detect when a gene had a pattern of expression which looked like it had a
503 boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient
504 similarity”. The formula is:
505 ∑
506 pixel<img src="cmsy8-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|
507 2 &#x22C5; pixel_value1 + pixel_value2
508 2
509 where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current pixel; &#x2220;&#x2207;i is the angle of the
510 gradient of image i at the current pixel; |&#x2207;i| is the magnitude of the gradient of image i at the current pixel; and
511 pixel valuei is the value of the current pixel in image i.
512 The intuition is that we want to see if the borders of the pattern in the two images are similar; if the borders
513 are similar, then both images will have corresponding pixels with large gradients (because this is a border) which
514 are oriented in a similar direction (because the borders are similar).
515 Gradient similarity provides information complementary to correlation
516 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses,
517 consider Fig. 3. The pointwise method in the top row identifies genes which express more strongly in AUD than
518 outside of it; its weakness is that this includes many areas which don&#8217;t have a salient border matching the areal
519 border. The geometric method identifies genes whose salient expression border seems to partially line up with
520 the border of AUD; its weakness is that this includes genes which don&#8217;t express over the entire area.
521 Areas which can be identified by single genes Using gradient similarity, we have already found single
522 genes which roughly identify some areas and groupings of areas. For each of these areas, an example of
523 a gene which roughly identifies it is shown in Figure 5. We have not yet cross-verified these genes in other
524 atlases.
525 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior
526 part of cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior
527 cingulate), VIS (visual), AUD (auditory).
528 These results validate our expectation that the ABA dataset can be exploited to find marker genes for many
529 cortical areas, while also validating the relevancy of our new scoring method, gradient similarity.
530 Combinations of multiple genes are useful and necessary for some areas
531 In Figure 4, we give an example of a cortical area which is not marked by any single gene, but which
532 can be identified combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for
533 predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left
534 picture in Figure 4 shows wwc1&#8217;s spatial expression pattern over the cortex. The lower-right boundary of MO is
535 represented reasonably well by this gene, but the gene overshoots the upper-left boundary. This flattened 2-D
536 representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex.
537 MO is only found on the dorsal surface. Gene mtif2 is shown in the upper-right. Mtif2 captures MO&#8217;s upper-left
538 boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding
539 together the values at each pixel in these two figures, we get the lower-left image. This combination captures
540 area MO much better than any single gene.
541 This shows that our proposal to develop a method to find combinations of marker genes is both possible and
542 necessary.
543 Multivariate supervised learning
544 Forward stepwise logistic regression Logistic regression is a popular method for predictive modeling of cate-
545 gorial data. As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise
546 logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify. This is
547 an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes
548 found were shown in various figures throughout this document, and Figure 4 shows a combination of genes
549 which was found.
550 SVM on all genes at once
551 In order to see how well one can do when looking at all genes at once, we ran a support vector machine to
552 classify cortical surface pixels based on their gene expression profiles. We achieved classification accuracy of
553 about 81%10. This shows that the genes included in the ABA dataset are sufficient to define much of cortical
554 anatomy. However, as noted above, a classifier that looks at all the genes at once isn&#8217;t as practically useful as a
555 classifier that uses only a few genes.
556 Data-driven redrawing of the cortical map
557 We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene ex-
558 pression profile associated with each pixel: Principal Components Analysis (PCA), Simple PCA, Multi-Dimensional
559 Scaling, Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment, Stochastic Proximity
560 Embedding, Fast Maximum Variance Unfolding, Non-negative Matrix Factorization (NNMF). Space constraints
561 prevent us from showing many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in
562 the first, second, and third rows of Figure 6.
563 After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we
564 have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are
565 shown in the last row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some
566 of the major subdivisions of cortex. These results clearly show that different dimensionality reduction techniques
567 capture different aspects of the data and lead to different clusterings, indicating the utility of our proposal to
568 produce a detailed comparion of these techniques as applied to the domain of genomic anatomy.
569 Many areas are captured by clusters of genes We also clustered the genes using gradient similarity to
570 see if the spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten
571 sample gene clusters, each cluster&#8217;s average expression pattern, compared to a known anatomical boundary.
572 This suggests that it is worth attempting to cluster genes, and then to use the results to cluster pixels.
573 The approach: what we plan to do
574 Flatmap cortex and segment cortical layers
575 There are multiple ways to flatten 3-D data into 2-D. We will compare mappings from manifolds to planes which
576 attempt to preserve size (such as the one used by Caret[7]) with mappings which preserve angle (conformal
577 maps). Our method will include a statistical test that warns the user if the assumption of 2-D structure seems to
578 be wrong.
579 We have not yet made use of radial profiles. While the radial profiles may be used &#8220;raw&#8221;, for laminar structures
580 like the cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would
581 then be associated with one expression level per gene per layer. We will develop a segmentation algorithm to
582 automatically identify the layer boundaries.
583 __
584 105-fold cross-validation.
585 Develop algorithms that find genetic markers for anatomical regions
586 Scoring measures and feature selection We will develop scoring methods for evaluating how good individual
587 genes are at marking areas. We will compare pointwise, geometric, and information-theoretic measures. We
588 already developed one entirely new scoring method (gradient similarity), but we may develop more. Scoring
589 measures that we will explore will include the L1 norm, correlation, expression energy ratio, conditional entropy,
590 gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such as Student&#8217;s t-
591 test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a scoring measure
592 on genes by taking the prediction error when using that gene to predict the target.
593 Using some combination of these measures, we will develop a procedure to find single marker genes for
594 anatomical regions: for each cortical area, we will rank the genes by their ability to delineate each area. We
595 will quantitatively compare the list of single genes generated by our method to the lists generated by previous
596 methods which are mentioned in Aim 1 Related Work.
597 Some cortical areas have no single marker genes but can be identified by combinatorial coding. This requires
598 multivariate scoring measures and feature selection procedures. Many of the measures, such as expression
599 energy, gradient similarity, Jaccard, Dice, Hough, Student&#8217;s t, and Mann-Whitney U are univariate. We will extend
600 these scoring measures for use in multivariate feature selection, that is, for scoring how well combinations of
601 genes, rather than individual genes, can distinguish a target area. There are existing multivariate forms of some
602 of the univariate scoring measures, for example, Hotelling&#8217;s T-square is a multivariate analog of Student&#8217;s t.
603 We will develop a feature selection procedure for choosing the best small set of marker genes for a given
604 anatomical area. In addition to using the scoring measures that we develop, we will also explore (a) feature
605 selection using a stepwise wrapper over &#8220;vanilla&#8221; classifiers such as logistic regression, (b) supervised learning
606 methods such as decision trees which incrementally/greedily combine single gene markers into sets, and (c)
607 supervised learning methods which use soft constraints to minimize number of features used, such as sparse
608 support vector machines.
609 Since errors of displacement and of shape may cause genes and target areas to match less than they should,
610 we will consider the robustness of feature selection methods in the presence of error. Some of these methods,
611 such as the Hough transform, are designed to be resistant in the presence of error, but many are not. We will
612 consider extensions to scoring measures that may improve their robustness; for example, a wrapper that runs a
613 scoring method on small displacements and distortions of the data adds robustness to registration error at the
614 expense of computation time.
615 An area may be difficult to identify because the boundaries are misdrawn in the atlas, or because the shape
616 of the natural domain of gene expression corresponding to the area is different from the shape of the area as
617 recognized by anatomists. We will extend our procedure to handle difficult areas by combining areas or redrawing
618 their boundaries. We will develop extensions to our procedure which (a) detect when a difficult area could be
619 fit if its boundary were redrawn slightly11, and (b) detect when a difficult area could be combined with adjacent
620 areas to create a larger area which can be fit.
621 A future publication on the method that we develop in Aim 1 will review the scoring measures and quantita-
622 tively compare their performance in order to provide a foundation for future research of methods of marker gene
623 finding. We will measure the robustness of the scoring measures as well as their absolute performance on our
624 dataset.
625 Classifiers We will explore and compare different classifiers. As noted above, this activity is not separate
626 from the previous one, because some supervised learning algorithms include feature selection, and any clas-
627 sifier can be combined with a stepwise wrapper for use as a feature selection method. We will explore logistic
628 regression (including spatial models[16]), decision trees12, sparse SVMs, generative mixture models (including
629 naive bayes), kernel density estimation, instance-based learning methods (such as k-nearest neighbor), genetic
630 _________________________________________
631 11Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by
632 multiple sources of evidence. Interestingly, the need to detect &#8220;natural spatial domains of gene expression&#8221; in a data-driven fashion
633 means that the methods of Aim 2 might be useful in achieving Aim 1, as well &#8211; particularly discriminative dimensionality reduction.
634 12Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision
635 tree for that area. We achieved good classification accuracy on our training set, but the number of genes that appeared in each tree was
636 too large. We plan to implement a pruning procedure to generate trees that use fewer genes.
637 algorithms, and artificial neural networks.
638 Develop algorithms to suggest a division of a structure into anatomical parts
639 Dimensionality reduction on gene expression profiles We have already described the application of ten
640 dimensionality reduction algorithms for the purpose of replacing the gene expression profiles, which are vectors
641 of about 4000 gene expression levels, with a smaller number of features. We plan to further explore and interpret
642 these results, as well as to apply other unsupervised learning algorithms, including independent components
643 analysis, self-organizing maps, and generative models such as deep Boltzmann machines. We will explore ways
644 to quantitatively compare the relevance of the different dimensionality reduction methods for identifying cortical
645 areal boundaries.
646 Dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene expression
647 profiles, the same techniques can be applied instead to the pixels13. It is possible that the features generated in
648 this way by some dimensionality reduction techniques will directly correspond to interesting spatial regions.
649 Clustering and segmentation on pixels We will explore clustering and segmentation algorithms in order to
650 segment the pixels into regions. We will explore k-means, spectral clustering, gene shaving[9], recursive division
651 clustering, multivariate generalizations of edge detectors, multivariate generalizations of watershed transforma-
652 tions, region growing, active contours, graph partitioning methods, and recursive agglomerative clustering with
653 various linkage functions. These methods can be combined with dimensionality reduction.
654 Clustering on genes We have already shown that the procedure of clustering genes according to gradient
655 similarity, and then creating an averaged prototype of each cluster&#8217;s expression pattern, yields some spatial
656 patterns which match cortical areas. We will further explore the clustering of genes.
657 In addition to using the cluster expression prototypes directly to identify spatial regions, this might be useful
658 as a component of dimensionality reduction. For example, one could imagine clustering similar genes and then
659 replacing their expression levels with a single average expression level, thereby removing some redundancy from
660 the gene expression profiles. One could then perform clustering on pixels (possibly after a second dimensionality
661 reduction step) in order to identify spatial regions. It remains to be seen whether removal of redundancy would
662 help or hurt the ultimate goal of identifying interesting spatial regions.
663 Co-clustering There are some algorithms which simultaineously incorporate clustering on instances and on
664 features (in our case, genes and pixels), for example, IRM[11]. These are called co-clustering or biclustering
665 algorithms.
666 Radial profiles We wil explore the use of the radial profile of gene expression under each pixel.
667 Compare different methods In order to tell which method is best for genomic anatomy, for each experimental
668 method we will compare the cortical map found by unsupervised learning to a cortical map derived from the Allen
669 Reference Atlas. We will explore various quantitative metrics that purport to measure how similar two clusterings
670 are, such as Jaccard, Rand index, Fowlkes-Mallows, variation of information, Larsen, Van Dongen, and others.
671 Discriminative dimensionality reduction In addition to using a purely data-driven approach to identify
672 spatial regions, it might be useful to see how well the known regions can be reconstructed from a small number
673 of features, even if those features are chosen by using knowledge of the regions. For example, linear discriminant
674 analysis could be used as a dimensionality reduction technique in order to identify a few features which are the
675 best linear summary of gene expression profiles for the purpose of discriminating between regions. This reduced
676 feature set could then be used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the
677 reference atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is.
678 _________________________________________
679 13Consider a matrix whose rows represent pixel locations, and whose columns represent genes. An entry in this matrix represents the
680 gene expression level at a given pixel. One can look at this matrix as a collection of pixels, each corresponding to a vector of many gene
681 expression levels; or one can look at it as a collection of genes, each corresponding to a vector giving that gene&#8217;s expression at each
682 pixel. Similarly, dimensionality reduction can be used to replace a large number of genes with a small number of features, or it can be
683 used to replace a large number of pixels with a small number of features.
684 Apply the new methods to the cortex
685 Using the methods developed in Aim 1, we will present, for each cortical area, a short list of markers to identify
686 that area; and we will also present lists of &#8220;panels&#8221; of genes that can be used to delineate many areas at once.
687 Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible for an unrelated
688 combination of genes to seem to identify an area when in fact it is only coincidence. There are two ways we will
689 validate our marker genes to guard against this. First, we will confirm that putative combinations of marker genes
690 express the same pattern in both hemispheres. Second, we will manually validate our final results on other gene
691 expression datasets such as EMAGE, GeneAtlas, and GENSAT[8].
692 Using the methods developed in Aim 2, we will present one or more hierarchial cortical maps. We will identify
693 and explain how the statistical structure in the gene expression data led to any unexpected or interesting features
694 of these maps, and we will provide biological hypotheses to interpret any new cortical areas, or groupings of
695 areas, which are discovered.
696 Timeline and milestones
697 Finding marker genes
698 September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers
699 November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information
700 for each layer
701 October 2009-April 2010: Develop scoring methods and to test them in various supervised learning frameworks.
702 Also test out various dimensionality reduction schemes in combination with supervised learning. create or extend
703 supervised learning frameworks which use multivariate versions of the best scoring methods.
704 January 2010 (milestone): Submit a publication on single marker genes for cortical areas
705 February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Explore the
706 best way to integrate radial profiles with supervised learning. Explore the best way to make supervised learning
707 techniques robust against incorrect labels (i.e. when the areas drawn on the input cortical map are slightly
708 off). Quantitatively compare the performance of different supervised learning techniques. Validate marker genes
709 found in the ABA dataset by checking against other gene expression datasets. Create documentation and unit
710 tests for software toolbox for Aim 1. Respond to user bug reports for Aim 1 software toolbox.
711 June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox.
712 July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a
713 small number of marker genes that can, in combination, define most of the areas at once
714 Revealing new ways to parcellate a structure into regions
715 June 2010-March 2011: Explore dimensionality reduction algorithms for Aim 2. Explore standard hierarchial
716 clustering algorithms, used in combination with dimensionality reduction, for Aim 2. Explore co-clustering algo-
717 rithms. Think about how radial profile information can be used for Aim 2. Adapt clustering algorithms to use radial
718 profile information. Quantitatively compare the performance of different dimensionality reduction and clustering
719 techniques. Quantitatively compare the value of different flatmapping methods and ways of representing radial
720 profiles.
721 March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox.
722 February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex. If
723 new ways of organizing the cortex into areas are discovered, read the literature and talk to people to learn about
724 research related to interpreting our results. Create documentation and unit tests for software toolbox for Aim 2.
725 Respond to user bug reports for Aim 2 software toolbox.
726 May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in
727 Aim 2
728 May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1.
729 Follow up on responses to our papers. Possibly submit another paper.
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