Layla Oesper: Great, thank you. I'm really excited to talk
to you today about some work we've been doing on inferring intra-tumor heterogeneity. So,
many types of tumors are highly heterogeneous, containing multiple distinct populations of
tumor cells, each with their own complement of somatic mutations. And this intra-tumor
heterogeneity arises because tumors evolve over time, and as different descendants of
the original or founding cell, acquire new mutations, which they then pass on to their
progeny.
Furthermore, many tumors also contain admixture by normal cells. And so there's been a number
of recent studies that have really begun to highlight the extent of intra-tumor heterogeneity,
using a variety of different methods from ultra-deep sequencing -- wrong button. All
right, so from ultra-deep sequencing, to multi-sectioning of different tumor samples, to even doing
further analysis of single tumor samples. And so given the proliferation of sequencing
data from modest coverage from many things like TCGA, this really led us to ask the question
of how can you really infer tumor composition from a single mixed tumor sample?
And there's been a lot of really exciting work in this area recently. And so most of
these methods fall into two different categories: the first is what I'll call SNV-based methods,
which utilize clustering of variant allele frequencies, or the fraction of rates that
indicate an SNV in order to determine tumor composition. However, because these methods
rely on looking at individual points in the genome, they often require higher coverage
enabled to overcome the variants in the data. So in contrast, there are also CAN-based methods,
which look at larger regions of the genome that have been potentially duplicated or deleted.
Two of the older and more popular methods are absolute and ascat [spelled phonetically];
however, both of these methods were originally designed for snipper rate data, and furthermore,
they don't explicitly consider multiple subclonal populations.
So let's actually take a look at how copy number aberrations effect sequencing data.
So, we generally identify copy number aberrations by looking at changes in read-depth over genomic
intervals, and so, so when we look at, in this example, at heterozygous deletion, we'll
actually see that this decrease in read-depth is proportional to the fraction of tumor cells
in the sample. So as the amount of tumor cells in the sample decreases, we actually see that
this change in read-depth actually decreases. Tumor samples also may contain multiple different
tumor populations, and so this type of intra-tumor heterogeneity has traditionally been viewed
as problematic when inferring copy number aberrations. However, as sequencing costs
have declined, the number of reads available to detect these subtle shifts in read-depth
have really made read-depth a really strong signal in sequencing data.
And so, especially for some of these larger copy number aberrations, where many thousands
to millions of read have been perturbed. Additionally, if a tumor population contains multiple copy
number aberrations, we expect this shift in read-depth to be consistent across all of
them. And so it's really these observations that have motivated the work that we've done
in our group. And so, in particular, we've devised a probabilistic model of sequencing
data when the different tumor populations contain different copy number aberrations.
So, consider this example here, where we have a true mixture of two different tumor populations,
and we've partitioned our genome into three equal length intervals, blue, red and yellow.
And so the data that we observe from a sequencing experiment would be read-depth information,
where we can count the number of reads that align to each one of these intervals in our
genomic partition. So what we'd really like to do is to be able to go from this observed
data to infer something about our true underlying mixture. And so, we're going to do this by
first parameterizing our true mixture using two parameters. So the first parameter is
what we call our interval count matrix C, and so in C, the columns are in integer values
that represent the number of copies of each genomic interval in each subpopulation in
the sample.
Our second parameter is actually going to be what we call a genome mixing vector mue
[spelled phonetically], which describes the proportion of the different subpopulations
in our mixture. So, if we know C and mue, we'd like to be able to infer something about
our observed read-depth information. So, let's take a look at -- a little closer into what
happens with our sequencing data. So, under typical assumptions we're going to assume
that our reads are sampled uniformly across the genomes in our sample, and so when we
do this, we observe that the probability of any read allowing to any particular interval
is going to be proportional to the amount of DNA from that interval in the entire tumor
sample. However, it's really important to note that these probabilities are not actually
independent values.
So consider the case of a relatively large dilution, so reads that no longer align to
this ratio because of the dilution actually may lead to an increase in observed read-depth
in other regions of the genome. So it's actually better to model this time of read-depth data
using a multinomial rather than independent binomials. So when we do this, we can actually
then measure or count the probability of a read aligning to any particular interval,
just using our parameters C and mue. So to complete our generative model, we then can
model our complete observed read-depth information as draws from a particular multinomial distribution,
again that depends only on our parameters C and mue.
So now, again, we'd like to be able to go this other direction, given observed information
about our read-depth, we want to be able to infer what are C and mue. And so we do this
using a maximum likelihood approach. However, it's important to note that this is actually
not an easily solvable problem, we actually had to devise a special coordinate transform
that allows us to solve this as a disjunction of different convects optimizations. I also
want to point out that the problem is actually not identifiable in C and mue, it's only identifiable
in the space of multinomial parameters, P.
So, we put this all together in our algorithm, which is called tumor heterogeneity analysis,
or THetA, and so THetA is a polynomial time algorithm in the case when we consider a single
tumor population in normal cells, and it can actually be extended to any number of tumor
populations, however I do have to note that when you have multiple tumor populations,
the run time is exponential in the number of intervals in your partition. So, to demonstrate
the efficacy of THetA let's look at some simulated data. So this is a simulation where I created
a mixture of three different tumor -- or different populations, normal cells and two different
tumor populations, in 43 percent of cells and 20 percent of cells, and so what you see
here are the actual copy number profiles for the different populations here, where the
color corresponds to the population it comes from.
So we applied THetA to this data set and found we did pretty well, so THetA inferred the
tumor purity within 3 percent of the true purity, and while there's some noise in the
copy number aberrations predicted, we were able to recover most of the large copy number
aberrations. So, we -- also for comparison, we applied absolute to this same simulation,
however I do want to note that while absolute has recently announced a new version, we weren't
actually able to get a copy of that due to licensing issues, so the results I'm showing
you here are actually from an older version. So absolute actually returns a collection
of different solutions with different purities and different likelihoods, which an analyst
can then go through and annotate, and so what I'm showing you here is a histogram of all
the purity values returned from all 12 solutions. And so the important thing to note is that
the bulk of them are actually much lower than the true purity of 63 percent. We also noticed
there's a parameter in absolute that allows you to set the maximum amount of DNA that
can be predicted as subclonal, and by default this is set to 5 percent, so we tried increasing
that to see if we'd get better solutions, and so while it returns many more solutions,
some of which are actually near the true value, the most likely solutions are still much lower.
So this is really demonstrating that it's really important to actually explicitly consider
multiple subclonal populations, in particular when trying to infer tumor purity. So we've
continued to do some work on THetA and I want to talk to you about three improvements that
we've done recently. So the first is we've actually done a lot to improve the optimization.
When we consider multiple tumor subpopulations, in fact it's over thousands of times faster
now than it used to be. We've also extended THetA to be applicable to both whole genome
and low pass sequencing data, and we've further done some refinements that allow us to measure
copy number aberrations at a more precise level, allowing us to do better analysis of
highly rearranged or highly segmented genomes. So I don't have time to talk about all three
of these, so I just want to show you some examples that really highlight the second
two points here.
So first off, we applied this data to a number of whole exome samples, and so for comparison,
we're comparing the purity of values inferred by THetA to purity values that were reported
by the original absolute paper using sniper rate data. And so for most of these we actually
find that our estimates of purity are actually quite similar, so if we actually take a look
at one of these samples where both algorithms return similar purity, we find that they both
have similar purity, if we apply THetA to whole genome data, again we get a similar
purity value.
However, in contrast to absolute, THetA was actually able to infer several subclonal aberrations
here, dilutions on chromosomes 3 and 13. So we wanted to do some further analysis to actually
make sure these were real, so we looked at read-depth information for the whole genome
data. So what we did was we partitioned the genome into 50 kb intervals, and what you
see here is the histogram of these read-depth ratios. So in this diagram, different peaks
correspond to different copy numbers in different populations of cells in the sample. So for
example, this big peak here corresponds to normal copy regions, we see amplifications,
dilutions that exist in all cells, but then we also see this other peak in between dilutions
and normal copy, which actually directly corresponds to the subclonal solutions that we predicted.
So there are also some samples where absolute appears to either underestimate purity or
in fact actually fails to predict purity at all do to high subclonality.
So this is one example of such a sample where THetA is actually able to infer information
about the different subpopulations. So as I mentioned, we've also applied THetA to low
past data, so here is a reconstruction for a pretty rearranged breast cancer genome.
We've looked at several other breast cancers with this as well. So moving on to my last
point, and so we've done some things that have allowed THetA to actually be applied
to really highly rearranged genomes, and so this is one example of a lung cancer genome
where we inferred two different populations in 50 percent and 18 percent of cells, and
we wanted to do some further analysis for this genome, so we created something that
we call a virtual snipper ray, and so what we do here is we identify heterozygous germline
snips from the matched normal, and we want to look at the observed allele frequency for
the minor allele or the B allele for the tumor genome. And so, let's actually consider here
chromosome six.
So chromosome six we predict to have normal copy, so we expect that it should contain
both copies of these alleles, so we'd expect that these B allele frequencies should be
centered right around 0.5, which is in fact exactly what we see. So now let's look at
a different chromosome, let's consider chromosome three here, where we've predicted it to be
deleted in all tumor cells in the population, so one copy of the allele has been deleted,
either the maternal or the paternal, so we'd expect that these B allele frequencies should
be centered right around close to either zero or one, which when we look at that is exactly
what we see. So then for any region that we've predicted to be subclonal dilution, where
it's only be diluted in a fraction of the tumor cells, we expect that B allele frequencies
should be not as far away from 0.5 but still -- and so that's exactly what we see for different
-- maybe. There we go. And that's exactly what we see for some of these different subclonal
aberrations that we've predicted.
So this is just an example where we've used B allele frequencies as a ways to do validation
of our estimates. We're also working on some things now where we actually want to incorporate
B allele frequencies into the model. So I briefly mentioned that there's an identifiability
issue, and so THetA might actually return to equally likely reconstructions when it's
used as just read-depth information, and so this is an example of a glioblastoma genome
where that happened. So we've devised a probabilistic model which uses the reconstructions output
by THetA in order to model the B allele frequencies, which we can then use to select the most likely
solution, and in this case we actually end up selecting the solution that is mostly diploid,
where we see some of these characteristic rearrangements from glioblastoma, like an
amplification of chromosome 7 or dilution of chromosome 10, and so going forward we're
looking at doing more with this and we really want to directly incorporate B allele frequencies
and SNVs directly into the THetA model.
So, in summary, I've described to you THetA, our algorithm for inferring tumor purity and
different tumor subpopulations, and I've introduced several improvements that we've done to THetA
that really allow us to apply to whole genome data including low past data as well as whole
like some data. And so with that I would like to thank my advisor, Ben Raphael, Gryte, who's
been working on some of these new improvements to THetA, and Ahmad who was involved in the
original development and the rest of the people from the Raphael research group. Thank you.
[applause]
Male Speaker: Time for one quick question.
Male Speaker: Oh, sorry, very nice talk. Have you tried
to incorporate mutation data into the THetA, because this is basically is a copy number
changes algorithm.
Layla Oesper: So yeah --
Male Speaker: Because there are some tumor types that are
basically very quiet.
Layla Oesper: Yeah so at this point we only are using the
read-depth information, and that's something that we want to do in the future, so if there
are different populations that are only distinguished by SNVs right now, THetA wouldn't be able
to distinguish those. That's a great question.
Male Speaker: Sorry, have you thought about any strategies
for how to validate the conclusions you get?
Layla Oesper: I mean, so we've used the B allele frequencies
at this point as our means of validation, so at this point that's actually not part
of the THetA model, so it's using different data in order to validate the reconstructions
that we've done.
Male Speaker: But that -- I don't think that can really
validate the clonal structures that you're arriving at.
Layla Oesper: Yeah, I mean, I think that's a hard question
in general, and probably requires, you know, maybe doing some amount of lab work at that
point, but yeah, it's definitely, I think, a hard question and something that, you know,
all the algorithms in this field have a problem with of how do you actually validate your
predictions?
Male Speaker: You talked about the thousand-fold improvement
in [unintelligible], what did that contribute to?
Layla Oesper: What did that what?
Male Speaker: What is the, what did you do to get the thousand
[unintelligible].
Layla Oesper: Yeah, yeah, so -- figure out how to do this
in one sentence. So basically we improved the way that we actually -- so we have enumerate
different of these C matrixes that are possible solutions, and so we were able to algorithmically
define a subset of them that could guarantee that we gain the optimal solution and we had
new ways of actually be able to enumerate those, and so rather than checking many more
of them or many fewer of them, exponentially less.
Male Speaker: Thank you.
Layla Oesper: I can tell you more in detail.
Male Speaker: Thank you Layla, very nice.
[applause]
Male Speaker: Our next --
[applause]
Male Speaker: -- presentation from Mike Gatza on the genomic
characterization of invasive lobular breast cancer. Mike?
[end of transcript]