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author bshanks@bshanks.dyndns.org
date Sat Apr 11 21:43:12 2009 -0700 (16 years ago)
parents 3bc61ab8e776
children 395faa66383e
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1 Specific aims
2 todo test4
3 Massive new datasets obtained with techniques such as in situ hybridization
4 (ISH) and BAC-transgenics allow the expression levels of many genes at many
5 locations to be compared. Our goal is to develop automated methods to relate
6 spatial variation in gene expression to anatomy. We want to find marker genes
7 for specific anatomical regions, and also to draw new anatomical maps based on
8 gene expression patterns. We have three specific aims:
9 (1) develop an algorithm to screen spatial gene expression data for combina-
10 tions of marker genes which selectively target anatomical regions
11 (2) develop an algorithm to suggest new ways of carving up a structure into
12 anatomical subregions, based on spatial patterns in gene expression
13 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains
14 a flattened version of the Allen Mouse Brain Atlas ISH data, as well as
15 the boundaries of cortical anatomical areas. Use this dataset to validate
16 the methods developed in (1) and (2).
17 In addition to validating the usefulness of the algorithms, the application of
18 these methods to cerebral cortex will produce immediate benefits, because there
19 are currently no known genetic markers for many cortical areas. The results
20 of the project will support the development of new ways to selectively target
21 cortical areas, and it will support the development of a method for identifying
22 the cortical areal boundaries present in small tissue samples.
23 All algorithms that we develop will be implemented in an open-source soft-
24 ware toolkit. The toolkit, as well as the machine-readable datasets developed
25 in aim (3), will be published and freely available for others to use.
26 Background and significance
27 Aim 1
28 Machine learning terminology
29 The task of looking for marker genes for anatomical subregions means that one
30 is looking for a set of genes such that, if the expression level of those genes is
31 known, then the locations of the subregions can be inferred.
32 If we define the subregions so that they cover the entire anatomical structure
33 to be divided, then instead of saying that we are using gene expression to find
34 the locations of the subregions, we may say that we are using gene expression to
35 determine to which subregion each voxel within the structure belongs. We call
36 this a classification task, because each voxel is being assigned to a class (namely,
37 its subregion).
38 1
40 Therefore, an understanding of the relationship between the combination of
41 their expression levels and the locations of the subregions may be expressed as
42 a function. The input to this function is a voxel, along with the gene expression
43 levels within that voxel; the output is the subregional identity of the target
44 voxel, that is, the subregion to which the target voxel belongs. We call this
45 function a classifier. In general, the input to a classifier is called an instance,
46 and the output is called a label.
47 The object of aim 1 is not to produce a single classifier, but rather to develop
48 an automated method for determining a classifier for any known anatomical
49 structure. Therefore, we seek a procedure by which a gene expression dataset
50 may be analyzed in concert with an anatomical atlas in order to produce a
51 classifier. Such a procedure is a type of a machine learning procedure. The
52 construction of the classifier is called training (also learning), and the initial
53 gene expression dataset used in the construction of the classifier is called training
54 data.
55 In the machine learning literature, this sort of procedure may be thought
56 of as a supervised learning task, defined as a task in whcih the goal is to learn
57 a mapping from instances to labels, and the training data consists of a set of
58 instances (voxels) for which the labels (subregions) are known.
59 Each gene expression level is called a feature, and the selection of which
60 genes to include is called feature selection. Feature selection is one component
61 of the task of learning a classifier. Some methods for learning classifiers start
62 out with a separate feature selection phase, whereas other methods combine
63 feature selection with other aspects of training.
64 One class of feature selection methods assigns some sort of score to each
65 candidate gene. The top-ranked genes are then chosen. Some scoring measures
66 can assign a score to a set of selected genes, not just to a single gene; in this
67 case, a dynamic procedure may be used in which features are added and sub-
68 tracted from the selected set depending on how much they raise the score. Such
69 procedures are called “stepwise” or “greedy”.
70 Although the classifier itself may only look at the gene expression data within
71 each voxel before classifying that voxel, the learning algorithm which constructs
72 the classifier may look over the entire dataset. We can categorize score-based
73 feature selection methods depending on how the score of calculated. Often
74 the score calculation consists of assigning a sub-score to each voxel, and then
75 aggregating these sub-scores into a final score (the aggregation is often a sum or
76 a sum of squares). If only information from nearby voxels is used to calculate a
77 voxel’s sub-score, then we say it is a local scoring method. If only information
78 from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a
79 pointwise scoring method.
80 Key questions when choosing a learning method are: What are the instances?
81 What are the features? How are the features chosen? Here are four principles
82 that outline our answers to these questions.
83 2
85 Principle 1: Combinatorial gene expression
86 Above, we defined an “instance” as the combination of a voxel with the “asso-
87 ciated gene expression data”. In our case this refers to the expression level of
88 genes within the voxel, but should we include the expression levels of all genes,
89 or only a few of them?
90 It is too much to hope that every anatomical region of interest will be iden-
91 tified by a single gene. For example, in the cortex, there are some areas which
92 are not clearly delineated by any gene included in the Allen Brain Atlas (ABA)
93 dataset. However, at least some of these areas can be delineated by looking
94 at combinations of genes (an example of an area for which multiple genes are
95 necessary and sufficient is provided in Preliminary Results).
96 Principle 2: Only look at combinations of small numbers of genes
97 When the classifier classifies a voxel, it is only allowed to look at the expression of
98 the genes which have been selected as features. The more data that is available
99 to a classifier, the better that it can do. For example, perhaps there are weak
100 correlations over many genes that add up to a strong signal. So, why not include
101 every gene as a feature? The reason is that we wish to employ the classifier in
102 situations in which it is not feasible to gather data about every gene. For
103 example, if we want to use the expression of marker genes as a trigger for some
104 regionally-targeted intervention, then our intervention must contain a molecular
105 mechanism to check the expression level of each marker gene before it triggers.
106 It is currently infeasible to design a molecular trigger that checks the level of
107 more than a handful of genes. Similarly, if the goal is to develop a procedure to
108 do ISH on tissue samples in order to label their anatomy, then it is infeasible
109 to label more than a few genes. Therefore, we must select only a few genes as
110 features.
111 Principle 3: Use geometry in feature selection
112 When doing feature selection with score-based methods, the simplest thing to do
113 would be to score the performance of each voxel by itself and then combine these
114 scores (pointwise scoring). A more powerful approach is to also use information
115 about the geometric relations between each voxel and its neighbors; this requires
116 non-pointwise, local scoring methods. See Preliminary Results for evidence of
117 the complementary nature of pointwise and local scoring methods.
118 Principle 4: Work in 2-D whenever possible
119 There are many anatomical structures which are commonly characterized in
120 terms of a two-dimensional manifold. When it is known that the structure that
121 one is looking for is two-dimensional, the results may be improved by allowing
122 the analysis algorithm to take advantage of this prior knowledge. In addition,
123 it is easier for humans to visualize and work with 2-D data.
124 Therefore, when possible, the instances should represent pixels, not voxels.
125 3
127 Aim 2
128 todo
129 Aim 3
130 Background
131 The cortex is divided into areas and layers. To a first approximation, the par-
132 cellation of the cortex into areas can be drawn as a 2-D map on the surface
133 of the cortex. In the third dimension, the boundaries between the areas con-
134 tinue downwards into the cortical depth, perpendicular to the surface. The layer
135 boundaries run parallel to the surface. One can picture an area of the cortex as
136 a slice of many-layered cake.
137 Although it is known that different cortical areas have distinct roles in both
138 normal functioning and in disease processes, there are no known marker genes
139 for many cortical areas. When it is necessary to divide a tissue sample into
140 cortical areas, this is a manual process that requires a skilled human to combine
141 multiple visual cues and interpret them in the context of their approximate
142 location upon the cortical surface.
143 Even the questions of how many areas should be recognized in cortex, and
144 what their arrangement is, are still not completely settled. A proposed division
145 of the cortex into areas is called a cortical map. In the rodent, the lack of a
146 single agreed-upon map can be seen by contrasting the recent maps given by
147 Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While
148 the maps are certainly very similar in their general arrangement, significant
149 differences remain in the details.
150 Significance
151 The method developed in aim (1) will be applied to each cortical area to find
152 a set of marker genes such that the combinatorial expression pattern of those
153 genes uniquely picks out the target area. Finding marker genes will be useful
154 for drug discovery as well as for experimentation because marker genes can be
155 used to design interventions which selectively target individual cortical areas.
156 The application of the marker gene finding algorithm to the cortex will
157 also support the development of new neuroanatomical methods. In addition to
158 finding markers for each individual cortical areas, we will find a small panel
159 of genes that can find many of the areal boundaries at once. This panel of
160 marker genes will allow the development of an ISH protocol that will allow
161 experimenters to more easily identify which anatomical areas are present in
162 small samples of cortex.
163 The method developed in aim (3) will provide a genoarchitectonic viewpoint
164 that will contribute to the creation of a better map. The development of present-
165 day cortical maps was driven by the application of histological stains. It is
166 conceivable that if a different set of stains had been available which identified
167 a different set of features, then the today’s cortical maps would have come out
168 4
170 differently. Since the number of classes of stains is small compared to the number
171 of genes, it is likely that there are many repeated, salient spatial patterns in
172 the gene expression which have not yet been captured by any stain. Therefore,
173 current ideas about cortical anatomy need to incorporate what we can learn
174 from looking at the patterns of gene expression.
175 While we do not here propose to analyze human gene expression data, it is
176 conceivable that the methods we propose to develop could be used to suggest
177 modifications to the human cortical map as well.
178 Related work
179 todo
180 Preliminary work
181 Justification of principles 1 thur 3
182 Principle 1: Combinatorial gene expression
183 Here we give an example of a cortical area which is not marked by any single
184 gene, but which can be identified combinatorially. according to logistic regres-
185 sion, gene wwc11 is the best fit single gene for predicting whether or not a pixel
186 on the cortical surface belongs to the motor area (area MO). The upper-left
187 picture in Figure shows wwc1’s spatial expression pattern over the cortex. The
188 lower-right boundary of MO is represented reasonably well by this gene, however
189 the gene overshoots the upper-left boundary. This flattened 2-D representation
190 does not show it, but the area corresponding to the overshoot is the medial
191 surface of the cortex. MO is only found on the lateral surface (todo).
192 Gnee mtif22 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s
193 upper-left boundary, but not its lower-right boundary. Mtif2 does not express
194 very much on the medial surface. By adding together the values at each pixel
195 in these two figures, we get the lower-left of Figure . This combination captures
196 area MO much better than any single gene.
197 Principle 2: Only look at combinations of small numbers of genes
198 In order to see how well one can do when looking at all genes at once, we ran
199 a support vector machine to classify cortical surface pixels based on their gene
200 expression profiles. We achieved classification accuracy of about 81%3. As noted
201 above, however, a classifier that looks at all the genes at once isn’t practically
202 useful.
203 _____________________
204 1“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
205 2“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
206 3Using the Shogun SVM package (todo:cite), with parameters type=GMNPSVM (multi-
207 class b-SVM), kernal = gaussian with sigma = 0.1, c = 10, epsilon = 1e-1 – these are the
208 first parameters we tried, so presumably performance would improve with different choices of
209 parameters. 5-fold cross-validation.
210 5
214 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2
215 (each pixel’s value on the lower left is the sum of the corresponding pixels in
216 the upper row). Within each picture, the vertical axis roughly corresponds to
217 anterior at the top and posterior at the bottom, and the horizontal axis roughly
218 corresponds to medial at the left and lateral at the right. The red outline is
219 the boundary of region MO. Pixels are colored approximately according to the
220 density of expressing cells underneath each pixel, with red meaning a lot of
221 expression and blue meaning little.
222 6
224 The requirement to find combinations of only a small number of genes limits
225 us from straightforwardly applying many of the most simple techniques from
226 the field of supervised machine learning. In the parlance of machine learning,
227 our task combines feature selection with supervised learning.
228 Principle 3: Use geometry
229 To show that local geometry can provide useful information that cannot be
230 detected via pointwise analyses, consider Fig. . The top row of Fig. displays
231 the 3 genes which most match area AUD, according to a pointwise method4. The
232 bottom row displays the 3 genes which most match AUD according to a method
233 which considers local geometry5 The pointwise method in the top row identifies
234 genes which express more strongly in AUD than outside of it; its weakness is that
235 this includes many areas which don’t have a salient border matching the areal
236 border. The geometric method identifies genes whose salient expression border
237 seems to partially line up with the border of AUD; its weakness is that this
238 includes genes which don’t express over the entire area. Genes which have high
239 rankings using both pointwise and border criteria, such as Aph1a in the example,
240 may be particularly good markers. None of these genes are, individually, a
241 perfect marker for AUD; we deliberately chose a “difficult” area in order to
242 better contrast pointwise with geometric methods.
243 Principle 4: Work in 2-D whenever possible
244 In anatomy, the manifold of interest is usually either defined by a combination
245 of two relevant anatomical axes (todo), or by the surface of the structure (as is
246 the case with the cortex). In the former case, the manifold of interest is a plane,
247 but in the latter case it is curved. If the manifold is curved, there are various
248 methods for mapping the manifold into a plane.
249 The method that we will develop will begin by mapping the data into a
250 2-D plane. Although the manifold that characterized cortical areas is known
251 to be the cortical surface, it remains to be seen which method of mapping the
252 manifold into a plane is optimal for this application. We will compare mappings
253 which attempt to preserve size (such as the one used by Caret??) with mappings
254 which preserve angle (conformal maps).
255 Although there is much 2-D organization in anatomy, there are also struc-
256 tures whose shape is fundamentally 3-dimensional. If possible, we would like
257 the method we develop to include a statistical test that warns the user if the
258 assumption of 2-D structure seems to be wrong.
259 ——
260 ____________________
261 4For each gene, a logistic regression in which the response variable was whether or not a
262 surface pixel was within area AUD, and the predictor variable was the value of the expression
263 of the gene underneath that pixel. The resulting scores were used to rank the genes in terms
264 of how well they predict area AUD.
265 5For each gene the gradient similarity (see section ??) between (a) a map of the expression
266 of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this
267 was used to rank the genes.
268 7
272 Figure 2: The top row shows the three genes which (individually) best predict
273 area AUD, according to logistic regression. The bottom row shows the three
274 genes which (individually) best match area AUD, according to gradient similar-
275 ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a,
276 Ptk7, Aph1a again, and Lepr
277 Massive new datasets obtained with techniques such as in situ hybridization
278 (ISH) and BAC-transgenics allow the expression levels of many genes at many
279 locations to be compared. This can be used to find marker genes for specific
280 anatomical structures, as well as to draw new anatomical maps. Our goal is
281 to develop automated methods to relate spatial variation in gene expression to
282 anatomy. We have five specific aims:
283 (1) develop an algorithm to screen spatial gene expression data for combi-
284 nations of marker genes which selectively target individual anatomical
285 structures
286 (2) develop an algorithm to screen spatial gene expression data for combina-
287 tions of marker genes which can be used to delineate most of the bound-
288 aries between a number of anatomical structures at once
289 (3) develop an algorithm to suggest new ways of dividing a structure up into
290 anatomical subregions, based on spatial patterns in gene expression
291 (4) create a flat (2-D) map of the mouse cerebral cortex that contains a flat-
292 tened version of the Allen Mouse Brain Atlas ISH dataset, as well as the
293 boundaries of anatomical areas within the cortex. For each cortical layer,
294 a layer-specific flat dataset will be created. A single combined flat dataset
295 will be created which averages information from all of the layers. These
296 datasets will be made available in both MATLAB and Caret formats.
297 (5) validate the methods developed in (1), (2) and (3) by applying them to
298 the cerebral cortex datasets created in (4)
299 8
301 All algorithms that we develop will be implemented in an open-source soft-
302 ware toolkit. The toolkit, as well as the machine-readable datasets developed in
303 aim (4) and any other intermediate dataset we produce, will be published and
304 freely available for others to use.
305 In addition to developing generally useful methods, the application of these
306 methods to cerebral cortex will produce immediate benefits that are only one
307 step removed from clinical application, while also supporting the development
308 of new neuroanatomical techniques. The method developed in aim (1) will be
309 applied to each cortical area to find a set of marker genes. Currently, despite
310 the distinct roles of different cortical areas in both normal functioning and
311 disease processes, there are no known marker genes for many cortical areas.
312 Finding marker genes will be immediately useful for drug discovery as well as for
313 experimentation because once marker genes for an area are known, interventions
314 can be designed which selectively target that area.
315 The method developed in aim (2) will be used to find a small panel of genes
316 that can find most of the boundaries between areas in the cortex. Today, finding
317 cortical areal boundaries in a tissue sample is a manual process that requires a
318 skilled human to combine multiple visual cues over a large area of the cortical
319 surface. A panel of marker genes will allow the development of an ISH protocol
320 that will allow experimenters to more easily identify which anatomical areas are
321 present in small samples of cortex.
322 For each cortical layer, a layer-specific flat dataset will be created. A single
323 combined flat dataset will be created which averages information from all of
324 the layers. These datasets will be made available in both MATLAB and Caret
325 formats.
326 ___________________________________________________________
327 New techniques allow the expression levels of many genes at many locations
328 to be compared. It is thought that even neighboring anatomical structures have
329 different gene expression profiles. We propose to develop automated methods
330 to relate the spatial variation in gene expression to anatomy. We will develop
331 two kinds of techniques:
332 (a) techniques to screen for combinations of marker genes which selectively
333 target anatomical structures
334 (b) techniques to suggest new ways of dividing a structure up into anatomical
335 subregions, based on the shapes of contours in the gene expression
336 The first kind of technique will be helpful for finding marker genes associated
337 with known anatomical features. The second kind of technique will be helpful in
338 creating new anatomical maps, maps which reflect differences in gene expression
339 the same way that existing maps reflect differences in histology.
340 We intend to develop our techniques using the adult mouse cerebral cortex
341 as a testbed. The Allen Brain Atlas has collected a dataset containing the
342 expression level of about 4000 genes* over a set of over 150000 voxels, with a
343 spatial resolution of approximately 200 microns[?].
344 9
346 We expect to discover sets of marker genes that pick out specific cortical
347 areas. This will allow the development of drugs and other interventions that
348 selectively target individual cortical areas. Therefore our research will lead
349 to application in drug discovery, in the development of other targeted clinical
350 interventions, and in the development of new experimental techniques.
351 The best way to divide up rodent cortex into areas has not been completely
352 determined, as can be seen by the differences in the recent maps given by Swan-
353 son on the one hand, and Paxinos and Franklin on the other. It is likely that our
354 study, by showing which areal divisions naturally follow from gene expression
355 data, as opposed to traditional histological data, will contribute to the creation
356 of a better map. While we do not here propose to analyze human gene expres-
357 sion data, it is conceivable that the methods we propose to develop could be
358 used to suggest modifications to the human cortical map as well.
359 In the following, we will only be talking about coronal data.
360 The Allen Brain Atlas provides “Smoothed Energy Volumes”, which are
361 One type of artifact in the Allen Brain Atlas data is what we call a “slice
362 artifact”. We have noticed two types of slice artifacts in the dataset. The first
363 type, a “missing slice artifact”, occurs when the ISH procedure on a slice did
364 not come out well. In this case, the Allen Brain investigators excluded the slice
365 at issue from the dataset. This means that no gene expression information is
366 available for that gene for the region of space covered by that slice. This results
367 in an expression level of zero being assigned to voxels covered by the slice. This
368 is partially but not completely ameliorated by the smoothing that is applied to
369 create the Smoothed Energy Volumes. The usual end result is that a region of
370 space which is shaped and oriented like a coronal slice is marked as having less
371 gene expression than surrounding regions.
372 The second type of slice artifact is caused by the fact that all of the slices
373 have a consistent orientation. Since there may be artifacts (such as how well
374 the ISH worked) which are constant within each slice but which vary between
375 different slices, the result is that ceteris paribus, when one compares the genetic
376 data of a voxel to another voxel within the same coronal plane, one would expect
377 to find more similarity than if one compared a voxel to another voxel displaced
378 along the rostrocaudal axis.
379 We are enthusiastic about the sharing of methods, data, and results, and
380 at the conclusion of the project, we will make all of our data and computer
381 source code publically available. Our goal is that replicating our results, or
382 applying the methods we develop to other targets, will be quick and easy for
383 other investigators. In order to aid in understanding and replicating our results,
384 we intend to include a software program which, when run, will take as input
385 the Allen Brain Atlas raw data, and produce as output all numbers and charts
386 found in publications resulting from the project.
387 To aid in the replication of our results, we will include a script which takes
388 as input the dataset in aim (3) and provides as output all of the tables in figures
389 in our publications .
390 We also expect to weigh in on the debate about how to best partition rodent
391 cortex
392 10
394 be useful for drug discovery as well
395 * Another 16000 genes are available, but they do not cover the entire cerebral
396 cortex with high spatial resolution.
397 User-definable ROIs Combinatorial gene expression Negative as well as pos-
398 itive signal Use geometry Search for local boundaries if necessary Flatmapped
399 Specific aims
400 Develop algorithms that find genetic markers for anatomical regions
401 1. Develop scoring measures for evaluating how good individual genes are at
402 marking areas: we will compare pointwise, geometric, and information-
403 theoretic measures.
404 2. Develop a procedure to find single marker genes for anatomical regions: for
405 each cortical area, by using or combining the scoring measures developed,
406 we will rank the genes by their ability to delineate each area.
407 3. Extend the procedure to handle difficult areas by using combinatorial cod-
408 ing: for areas that cannot be identified by any single gene, identify them
409 with a handful of genes. We will consider both (a) algorithms that incre-
410 mentally/greedily combine single gene markers into sets, such as forward
411 stepwise regression and decision trees, and also (b) supervised learning
412 techniques which use soft constraints to minimize the number of features,
413 such as sparse support vector machines.
414 4. Extend the procedure to handle difficult areas by combining or redrawing
415 the boundaries: An area may be difficult to identify because the bound-
416 aries are misdrawn, or because it does not “really” exist as a single area,
417 at least on the genetic level. We will develop extensions to our procedure
418 which (a) detect when a difficult area could be fit if its boundary were
419 redrawn slightly, and (b) detect when a difficult area could be combined
420 with adjacent areas to create a larger area which can be fit.
421 Apply these algorithms to the cortex
422 1. Create open source format conversion tools: we will create tools to bulk
423 download the ABA dataset and to convert between SEV, NIFTI and MAT-
424 LAB formats.
425 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw
426 the cortical area boundaries onto it.
427 3. Find layer boundaries: cluster similar voxels together in order to auto-
428 matically find the cortical layer boundaries.
429 4. Run the procedures that we developed on the cortex: we will present, for
430 each area, a short list of markers to identify that area; and we will also
431 11
433 present lists of “panels” of genes that can be used to delineate many areas
434 at once.
435 Develop algorithms to suggest a division of a structure into anatom-
436 ical parts
437 1. Explore dimensionality reduction algorithms applied to pixels: including
438 TODO
439 2. Explore dimensionality reduction algorithms applied to genes: including
440 TODO
441 3. Explore clustering algorithms applied to pixels: including TODO
442 4. Explore clustering algorithms applied to genes: including gene shaving,
443 TODO
444 5. Develop an algorithm to use dimensionality reduction and/or hierarchial
445 clustering to create anatomical maps
446 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic
447 map of the cortex
448 gradient similarity is calculated as: ∑
449 pixels cos(abs(∠∇1 - ∠∇2)) ⋅|∇1|+|∇2|
450 2 ⋅
451 pixel_value1+pixel_value2
452 2
453 (todo) Technically, we say that an anatomical structure has a fundamen-
454 tally 2-D organization when there exists a commonly used, generic, anatomical
455 structure-preserving map from 3-D space to a 2-D manifold.
456 Related work:
457 The Allen Brain Institute has developed an interactive web interface called
458 AGEA which allows an investigator to (1) calculate lists of genes which are se-
459 lectively overexpressed in certain anatomical regions (ABA calls this the “Gene
460 Finder” function) (2) to visualize the correlation between the genetic profiles of
461 voxels in the dataset, and (3) to visualize a hierarchial clustering of voxels in
462 the dataset [?]. AGEA is an impressive and useful tool, however, it does not
463 solve the same problems that we propose to solve with this project.
464 First we describe AGEA’s “Gene Finder”, and then compare it to our pro-
465 posed method for finding marker genes. AGEA’s Gene Finder first asks the
466 investigator to select a single “seed voxel” of interest. It then uses a clustering
467 method, combined with built-in knowledge of major anatomical structures, to
468 select two sets of voxels; an “ROI” and a “comparator region”*. The seed voxel
469 is always contained within the ROI, and the ROI is always contained within the
470 comparator region. The comparator region is similar but not identical to the
471 set of voxels making up the major anatomical region containing the ROI. Gene
472 Finder then looks for genes which can distinguish the ROI from the comparator
473 region. Specifically, it finds genes for which the ratio (expression energy in the
474 ROI) / (expression energy in the comparator region) is high.
475 12
477 Informally, the Gene Finder first infers an ROI based on clustering the seed
478 voxel with other voxels. Then, the Gene Finder finds genes which overexpress
479 in the ROI as compared to other voxels in the major anatomical region.
480 There are three major differences between our approach and Gene Finder.
481 First, Gene Finder focuses on individual genes and individual ROIs in isola-
482 tion. This is great for regions which can be picked out from all other regions by a
483 single gene, but not all of them can (todo). There are at least two ways this can
484 miss out on useful genes. First, a gene might express in part of a region, but not
485 throughout the whole region, but there may be another gene which expresses
486 in the rest of the region*. Second, a gene might express in a region, but not in
487 any of its neighbors, but it might express also in other non-neighboring regions.
488 To take advantage of these types of genes, we propose to find combinations of
489 genes which, together, can identify the boundaries of all subregions within the
490 containing region.
491 Second, Gene Finder uses a pointwise metric, namely expression energy ratio,
492 to decide whether a gene is good for picking out a region. We have found better
493 results by using metrics which take into account not just single voxels, but also
494 the local geometry of neighboring voxels, such as the local gradient (todo). In
495 addition, we have found that often the absence of gene expression can be used
496 as a marker, which will not be caught by Gene Finder’s expression energy ratio
497 (todo).
498 Third, Gene Finder chooses the ROI based only on the seed voxel. This
499 often does not permit the user to query the ROI that they are interested in. For
500 example, in all of our tests of Gene Finder in cortex, the ROIs chosen tend to
501 be cortical layers, rather than cortical areas.
502 In summary, when Gene Finder picks the ROI that you want, and when this
503 ROI can be easily picked out from neighboring regions by single genes which
504 selectively overexpress in the ROI compared to the entire major anatomical re-
505 gion, Gene Finder will work. However, Gene Finder will not pick cortical areas
506 as ROIs, and even if it could, many cortical areas cannot be uniquely picked out
507 by the overexpression of any single gene. By contrast, we will target cortical
508 areas, we will explore a variety of metrics which can complement the shortcom-
509 ings of expression energy ratio, and we will use the combinatorial expression of
510 genes to pick out cortical areas even when no individual gene will do.
511 * The terms “ROI” and “comparator region” are our own; the ABI calls
512 them the “local region” and the “larger anatomical context”. The ABI uses the
513 term “specificity comparator” to mean the major anatomic region containing
514 the ROI, which is not exactly identical to the comparator region.
515 ** In this case, the union of the area of expression of the two genes would
516 suffice; one could also imagine that there could be situations in which the in-
517 tersection of multiple genes would be needed, or a combination of unions and
518 intersections.
519 Now we describe AGEA’s hierarchial clustering, and compare it to our pro-
520 posal. The goal of AGEA’s hierarchial clustering is to generate a binary tree of
521 clusters, where a cluster is a collection of voxels. AGEA begins by computing
522 the Pearson correlation between each pair of voxels. They then employ a recur-
523 13
525 sive divisive (top-down) hierarchial clustering procedure on the voxels, which
526 means that they start with all of the voxels, and then they divide them into clus-
527 ters, and then within each cluster, they divide that cluster into smaller clusters,
528 etc***. At each step, the collection of voxels is partitioned into two smaller
529 clusters in a way that maximizes the following quantity: average correlation
530 between all possible pairs of voxels containing one voxel from each cluster.
531 There are three major differences between our approach and AGEA’s hier-
532 archial clustering. First, AGEA’s clustering method separates cortical layers
533 before it separates cortical areas.
534 following procedure is used for the purpose of dividing a collection of voxels
535 into smaller clusters: partition the voxels into two sets, such that the following
536 quantity is maximized:
537 *** depending on which level of the tree is being created, the voxels are
538 subsampled in order to save time
539 does not allow the user to input anything other than a seed voxel; this means
540 that for each seed voxel, there is only one
541 The role of the “local region” is to serve as a region of interest for which
542 marker genes are desired; the role of the “larger anatomical context” is to be
543 the structure
544 There are two kinds of differences between AGEA and our project; differ-
545 ences that relate to the treatment of the cortex, and differences in the type of
546 generalizable methods being developed. As relates
547 indicate an ROI
548 explore simple correlation-based relationships between voxels, genes, and
549 clusters of voxels.
550 There have not yet been any studies which describe the results of applying
551 AGEA to the cerebral cortex; however, we suspect that the AGEA metrics are
552 not optimal for the task of relating genes to cortical areas. A voxel’s gene
553 expression profile depends upon both its cortical area and its cortical layer,
554 however, AGEA has no mechanism to distinguish these two. As a result, voxels
555 in the same layer but different areas are often clustered together by AGEA. As
556 part of the project, we will compare the performance of our techniques against
557 AGEA’s.
558 —
559 The Allen Brain Institute has developed interactive tools called AGEA which
560 allow an investigator to explore simple correlation-based relationships between
561 voxels, genes, and clusters of voxels. There have not yet been any studies
562 which describe the results of applying AGEA to the cerebral cortex; however,
563 we suspect that the AGEA metrics are not optimal for the task of relating
564 genes to cortical areas. A voxel’s gene expression profile depends upon both
565 its cortical area and its cortical layer, however, AGEA has no mechanism to
566 distinguish these two. As a result, voxels in the same layer but different areas
567 are often clustered together by AGEA. As part of the project, we will compare
568 the performance of our techniques against AGEA’s.
569 Another difference between our techniques and AGEA’s is that AGEA allows
570 the user to enter only a voxel location, and then to either explore the rest of
571 14
573 the brain’s relationship to that particular voxel, or explore a partitioning of
574 the brain based on pairwise voxel correlation. If the user is interested not in a
575 single voxel, but rather an entire anatomical structure, AGEA will only succeed
576 to the extent that the selected voxel is a typical representative of the structure.
577 As discussed in the previous paragraph, this poses problems for structures like
578 cortical areas, which (because of their division into cortical layers) do not have
579 a single “typical representative”.
580 By contrast, in our system, the user will start by selecting, not a single voxel,
581 but rather, an anatomical superstructure to be divided into pieces (for example,
582 the cerebral cortex). We expect that our methods will take into account not
583 just pairwise statistics between voxels, but also large-scale geometric features
584 (for example, the rapidity of change in gene expression as regional boundaries
585 are crossed) which optimize the discriminability of regions within the selected
586 superstructure.
587 —–
588 screen for combinations of marker genes which selectively target anatom-
589 ical structures pick delineate the boundaries between neighboring anatomical
590 structures. (b) techniques to screen for marker genes which pick out anatomical
591 structures of interest
592 , techniques which: (a) screen for marker genes , and (b) suggest new
593 anatomical maps based on
594 whose expression partitions the region of interest into its anatomical sub-
595 structures, and (b) use the natural contours of gene expression to suggest new
596 ways of dividing an organ into
597 The Allen Brain Atlas
598 –
599 to: brooksl@mail.nih.gov
600 Hi, I’m writing to confirm the applicability of a potential research project to
601 the challenge grant topic ”New computational and statistical methods for the
602 analysis of large data sets from next-generation sequencing technologies”.
603 We want to develop methods for the analysis of gene expression datasets that
604 can be used to uncover the relationships between gene expression and anatomical
605 regions. Specifically, we want to develop techniques to (a) given a set of known
606 anatomical areas, identify genetic markers for each of these areas, and (b) given
607 an anatomical structure whose substructure is unknown, suggest a map, that
608 is, a division of the space into anatomical sub-structures, that represents the
609 boundaries inherent in the gene expression data.
610 We propose to develop our techniques on the Allen Brain Atlas mouse brain
611 gene expression dataset by finding genetic markers for anatomical areas within
612 the cerebral cortex. The Allen Brain Atlas contains a registered 3-D map of
613 gene expression data with 200-micron voxel resolution which was created from
614 in situ hybridization data. The dataset contains about 4000 genes which are
615 available at this resolution across the entire cerebral cortex.
616 Despite the distinct roles of different cortical areas in both normal function-
617 ing and disease processes, there are no known marker genes for many cortical
618 areas. This project will be immediately useful for both drug discovery and clini-
619 15
621 cal research because once the markers are known, interventions can be designed
622 which selectively target specific cortical areas.
623 This techniques we develop will be useful because they will be applicable to
624 the analysis of other anatomical areas, both in terms of finding marker genes
625 for known areas, and in terms of suggesting new anatomical subdivisions that
626 are based upon the gene expression data.
627 _______________________________
628 It is likely that our study, by showing which areal divisions naturally fol-
629 low from gene expression data, as opposed to traditional histological data, will
630 contribute to the creation of
631 there are clear genetic or chemical markers known for only a few cortical
632 areas. This makes it difficult to target drugs to specific
633 As part of aims (1) and (5), we will discover sets of marker genes that pick
634 out specific cortical areas. This will allow the development of drugs and other
635 interventions that selectively target individual cortical areas. As part of aims
636 (2) and (5), we will also discover small panels of marker genes that can be used
637 to delineate most of the cortical areal map.
638 With aims (2) and (4), we
639 There are five principals
640 In addition to validating the usefulness of the algorithms, the application of
641 these methods to cerebral cortex will produce immediate benefits that are only
642 one step removed from clinical application.
643 todo: remember to check gensat, etc for validation (mention bias/variance)
644 Why it is useful to apply these methods to cortex
645 There is still room for debate as to exactly how the cortex should be parcellated
646 into areas.
647 The best way to divide up rodent cortex into areas has not been completely
648 determined,
649 not yet been accounted for in
650 that the expression of some genes will contain novel spatial patterns which
651 are not account
652 that a genoarchitectonic map
653 This principle is only applicable to aim 1 (marker genes). For aim 2 (partition
654 a structure in into anatomical subregions), we plan to work with many genes at
655 once.
656 tood: aim 2 b+s?
657 Principle 5: Interoperate with existing tools
658 In order for our software to be as useful as possible for our users, it will be
659 able to import and export data to standard formats so that users can use our
660 software in tandem with other software tools created by other teams. We will
661 support the following formats: NIFTI (Neuroimaging Informatics Technology
662 16
664 Initiative), SEV (Allen Brain Institute Smoothed Energy Volume), and MAT-
665 LAB. This ensures that our users will not have to exclusively rely on our tools
666 when analyzing data. For example, users will be able to use the data visualiza-
667 tion and analysis capabilities of MATLAB and Caret alongside our software.
668 To our knowledge, there is no currently available software to convert between
669 these formats, so we will also provide a format conversion tool. This may be
670 useful even for groups that don’t use any of our other software.
671 todo: is “marker gene” even a phrase that we should use at all?
672 note for aim 1 apps: combo of genes is for voxel, not within any single cell
673 , as when genetic markers allow the development of selective interventions;
674 the reason that one can be confident that the intervention is selective is that it
675 is only turned on when a certain combination of genes is turned on and off. The
676 result procedure is what assures us that when that combination is present, the
677 local tissue is probably part of a certain subregion.
678 The basic idea is that we want to find a procedure by
679 The task of finding genes that mark anatomical areas can be phrased in
680 terms of what the field of machine learning calls a “supervised learning” task.
681 The goal of this task is to learn a function (the “classifier”) which
682 If a person knows a combination of genes that mark an area, that implies
683 that the person can be told how strong those genes express in any voxel, and
684 the person can use this information to determine how
685 finding how to infer the areal identity of a voxel if given the gene expression
686 profile of that voxel.
687 For each voxel in the cortex, we want to start with data about the gene
688 expression
689 There are various ways to look for marker genes. We will define some terms,
690 and along the way we will describe a few design choices encountered in the
691 process of creating a marker gene finding method, and then we will present four
692 principles that describe which options we have chosen.
693 In developing a procedure for finding marker genes, we are developing a
694 procedure that takes a dataset of experimental observations and produces a
695 result. One can think of the result as merely a list of genes, but really the result
696 is an understanding of a predictive relationship between, on the one hand, the
697 expression levels of genes, and, on the other hand, anatomical subregions.
698 One way to more formally define this understanding is to look at it as a
699 procedure. In this view, the result of the learning procedure is itself a procedure.
700 The result procedure provides a way to use the gene expression profiles of voxels
701 in a tissue sample in order to determine where the subregions are.
702 This result procedure can be used directly, as when an experimenter has
703 a tissue sample and needs to know what subregions are present in it, and,
704 if multiple subregions are present, where they each are. Or it can be used
705 indirectly; imagine that the result procedure tells us that whenever a certain
706 combination of genes are expressed, the local tissue is probably part of a certain
707 subregion. This means that we can then confidentally develop an intervention
708 which is triggered only when that combination of genes are expressed; and to
709 17
711 the extent that the result procedure is reliable, we know that the intervention
712 will only be triggered in the target subregion.
713 We said that the result procedure provides “a way to use the gene expression
714 profiles of voxels in a tissue sample” in order to “determine where the subregions
715 are”.
716 Does the result procedure get as input all of the gene expression profiles
717 of each voxel in the entire tissue sample, and produce as output all of the
718 subregional boundaries all at once?
719 it is helpful for the classifier to look at the global “shape” of gene expression
720 patterns over the whole structure, rather than just nearby voxels.
721 there is some small bit of additional information that can be gleaned from
722 knowing the
723 Design choices for a supervised learning procedure
724 After all,
725 there is a small correlation between the gene expression levels from distant
726 voxels and
727 Depending on how we intend to use the classifier, we may want to design it
728 so that
729 It is possible for many things to
730 The choice of which data is made part of an instance
731 what we seek is a procedure
732 partition the tissue sample into subregions.
733 each part of the anatomical structure
734 must be One way to rephrase this task is to say that, instead of searching
735 for the location of the subregions, we are looking to partition the tissue sample
736 into subregions.
737 There are various ways to look for marker genes. We will define some terms,
738 and along the way we will describe a few design choices encountered in the
739 process of creating a marker gene finding method, and then we will present four
740 principles that describe which options we have chosen.
741 In developing a procedure for finding marker genes, we are developing a
742 procedure that takes a dataset of experimental observations and produces a
743 result. One can think of the result as merely a list of genes, but really the result
744 is an understanding of a predictive relationship between, on the one hand, the
745 expression levels of genes, and, on the other hand, anatomical subregions.
746 One way to more formally define this understanding is to look at it as a
747 procedure. In this view, the result of the learning procedure is itself a procedure.
748 The result procedure provides a way to use the gene expression profiles of voxels
749 in a tissue sample in order to determine where the subregions are.
750 This result procedure can be used directly, as when an experimenter has
751 a tissue sample and needs to know what subregions are present in it, and,
752 if multiple subregions are present, where they each are. Or it can be used
753 indirectly; imagine that the result procedure tells us that whenever a certain
754 combination of genes are expressed, the local tissue is probably part of a certain
755 18
757 subregion. This means that we can then confidentally develop an intervention
758 which is triggered only when that combination of genes are expressed; and to
759 the extent that the result procedure is reliable, we know that the intervention
760 will only be triggered in the target subregion.
761 We said that the result procedure provides “a way to use the gene expression
762 profiles of voxels in a tissue sample” in order to “determine where the subregions
763 are”.
764 Does the result procedure get as input all of the gene expression profiles
765 of each voxel in the entire tissue sample, and produce as output all of the
766 subregional boundaries all at once?
767 Or are we given one voxel at a time,
768 In the jargon of the field of machine learning, the result procedure is called
769 a classifier.
770 The task of finding genes that mark anatomical areas can be phrased in
771 terms of what the field of machine learning calls a “supervised learning” task.
772 The goal of this task is to learn a function (the “classifier”) which
773 If a person knows a combination of genes that mark an area, that implies
774 that the person can be told how strong those genes express in any voxel, and
775 the person can use this information to determine how
776 finding how to infer the areal identity of a voxel if given the gene expression
777 profile of that voxel.
778 For each voxel in the cortex, we want to start with data about the gene
779 expression
780 single voxels, but rather groups of voxels, such that the groups can be placed
781 in some 2-D space. We will call such instances “pixels”.
782 We have been speaking as if instances necessarily correspond to single voxels.
783 But it is possible for instances to be groupings of many voxels, in which case
784 each grouping must be assigned the same label (that is, each voxel grouping
785 must stay inside a single anatomical subregion).
786 In some but not all cases, the groups are either rows or columns of voxels.
787 This is the case with the cerebral cortex, in which one may assume that columns
788 of voxels which run perpendicular to the cortical surface all share the same areal
789 identity. In the cortex, we call such an instance a “surface pixel”, because such
790 an instance represents the data associated with all voxels underneath a specific
791 patch of the cortical surface.
792 19