A Melanoma Brain Metastasis with a Donor-Patient Hybrid Genome following Bone Marrow Transplantation: First Evidence for Fusion in Human Cancer

Background Tumor cell fusion with motile bone marrow-derived cells (BMDCs) has long been posited as a mechanism for cancer metastasis. While there is much support for this from cell culture and animal studies, it has yet to be confirmed in human cancer, as tumor and marrow-derived cells from the same patient cannot be easily distinguished genetically. Methods We carried out genotyping of a metastatic melanoma to the brain that arose following allogeneic bone-marrow transplantation (BMT), using forensic short tandem repeat (STR) length-polymorphisms to distinguish donor and patient genomes. Tumor cells were isolated free of leucocytes by laser microdissection, and tumor and pre-transplant blood lymphocyte DNAs were analyzed for donor and patient alleles at 14 autosomal STR loci and the sex chromosomes. Results All alleles in the donor and patient pre-BMT lymphocytes were found in tumor cells. The alleles showed disproportionate relative abundances in similar patterns throughout the tumor, indicating the tumor was initiated by a clonal fusion event. Conclusions Our results strongly support fusion between a BMDC and a tumor cell playing a role in the origin of this metastasis. Depending on the frequency of such events, the findings could have important implications for understanding the generation of metastases, including the origins of tumor initiating cells and the cancer epigenome.


Lazova et al. A melanoma metastasis with a donor-patient hybrid genome: Forensic evidence for fusion in human cancer
Statistical Modeling and Analysis

Data
We focused on the six loci having both patient-specific and donor-specific alleles, since they seemed the most informative for the questions considered below. Each of these six loci also happened to have one shared allele. A graphical display of the RFU data for these loci is shown in Fig. S6. Allele peaks that did not reach a height of at least 50 Relative Florescence units (RFU) were not called as 'alleles' and were not scored with numeric values, due to questions about validity below 50 RFU, which in this genotyping system is considered a qualitative threshold for signal to noise reasons. Therefore, our models treated such allelic peaks as left-censored (1); that is, only the information that the peak value was less than 50 RFU was used.

Implausibility of contamination: a first approach
An alternative potential explanation for the presence of donor-specific alleles is that, despite extensive procedural precautions and pathological analyses described in the text, our tumor samples were contaminated by leukocytes, ultimately derived from the donor. However, simple numerical observations suggest this is unlikely. For 1, , 9 s =  , let s d denote the donor contamination ratio for section s, defined to be the ratio of the number of donor leukocytes to the number of patient cancer cells in section s. A simple indication of contamination levels necessary to explain the donor alleles is given by ratios of donorspecific alleles to patient-specific alleles. Let sl P and sl D denote, respectively, the patient-and donor-specific allelic peaks (measured in RFU) in section s at locus l , and let l i denote the number of patient-specific alleles at locus l in each patient cancer cell (which may be greater than 1, e.g., due to aneuploidy). Letting s n denote the number of patient cancer cells in section s , if each of these cells has l i patient-specific alleles at locus l , there will be a total of s l n i patient-specific alleles. By definition, there are also

Statistical Models of fusion and contamination
The preceding considerations suggest that the credibility of donor contamination as an explanation for the donor alleles is low. To provide a more quantitative probabilistic analysis, we assumed that deviations from exact equality in expected approximations such as sl s sl l D P i d » may be described by statistical distributions. We fit a number of Bayesian statistical models (2) to the data for the six loci showing both patient and donor specific alleles. Here we will report in detail on two models, referred to as "fusion" and "contamination," which assumed that the donor alleles are explained by fusion and by donor contamination, respectively.
We modeled the RFU intensity for each allele at a given locus and section as a random variable with a Normal distribution whose mean is proportional to the number of such alleles present in the section, and whose variance incorporates both additive and multiplicative random perturbations. To describe the models, let P , S , and D generically denote patient-specific, shared, and donor-specific alleles in genotypes. In the fusion model, the cancer cells are hybrids resulting from fusion, and at locus l we assumed the cancer cells have genotypes of the form Together with the assumption that the expected value of an allelic peak should be proportional to the number of copies of that allele in the section, this leads to The expressions for the variances allow the allelic peaks to be subject to additive and multiplicative random perturbations. These expressions arise by assuming, for example, , and so the above expressions for the means are replaced by Bayesian models require prior distributions for all unknown parameters. We assumed the total intensities sl l were drawn from an Exponential distribution with mean 10,000, modeling diffuse prior distributions spread over a wide range. Patient and donor contamination levels were assumed to come from Exponential distributions truncated at an upper bound of 0.2. Pathology studies concluding that contamination levels are probably less than 0.01 and very unlikely to be as high as 0.05 support confidence in 0.2 as a conservative upper bound. The Exponential shape was again meant to be conservative, allowing high probabilities for contamination levels up to 0.2 (in fact this choice hardly differs from a uniform distribution on that interval). The additive standard deviation add s was taken to have a half-Cauchy distribution with scale parameter 25 (3), and the multiplicative variance 2 mult s , a uniform distribution on the interval from 0 to 0.25. Finally, for cancer cells, we need a prior for the number of copies of each allele at each locus, that is, a probability distribution governing the numbers l i , l j , and l k . To check for undesirable sensitivity to this choice we repeated our analysis with the two different distributions p1 and p2 whose probabilities are shown in Table S2 Table S2. Two prior distributions for allelic copy numbers in cancer cells.
These distributions incorporate the aneuploidy that occurs in cancer cells, so that alleles can be lost or gained. Such losses and gains are less likely in distribution p2 than they are in p1. In both distributions, increasing copy numbers of 2 through 10 are assigned decreasing probabilities. These p2 probabilities decrease more quickly than the p1 probabilities, so that p2 assigns much smaller probability to high copy numbers than p1 does. To avoid duplication we will report results in detail mainly for distribution p1; in fact the conclusions turned out to be the same using both distributions, showing stability and lack of sensitivity to these different choices of prior distribution.

Model fitting
The models were fit by Markov chain Monte Carlo (MCMC, e.g., (4)), using the software JAGS (5). We used two different run lengths for different models: shorter runs of 110,000 iterations with the first 10,000 iterations discarded as "burn-in", and 1,100,000 iterations with the first 100,000 iterations discarded. The shorter runs were used in many initial investigations of new models and also in creating the calibration distributions in the computationally intensive calibration procedure described below. Informal checks of time-series plots of the parameters as well as the deviances (defined as twice the negative log likelihood; smaller deviance indicates better fit) indicated that in fact very little burnin was needed and the amount discarded was more than enough. The longer runs were used for extra accuracy and to increase certainty that better regions of the parameter space were not being missed. The longer runs were also used in establishing good initial values for the shorter runs in the calibration distributions, and choosing these initial values helped the shorter runs to work well. Fig. S7 shows plots of the deviances obtained by two of the longer runs. They support confidence that the mixing of the Markov chains is satisfactory. The result of each MCMC run for a given model is a sample of parameter values approximately from the posterior distribution for that model, and the distributions of these samples are summarized in the following figures. We begin with the fusion model. The next figure shows the posterior samples for the allele counts of the patient-specific, shared, and donor-specific alleles. It suggests, for example, that at the FGA locus, the fusion cells had several copies of the patient-specific and shared alleles, and one copy of the donor specific allele, and at the D13S317 locus, the patient-specific allele was lost in the fusion cell.
The distributions of the patient contamination levels are summarized in the following histograms.

D19S433 donor
These distributions are not so different from the assumed prior, indicating that the data are not very informative about these parameters. The additive and multiplicative error distributions are described by the following histograms.
These suggest that the additive standard deviation is around 30 RFU or so, and the multiplicative error standard deviation is on the order of 10 to 15 percent or so.
We calculated standardized Bayesian residuals defined by

D19S433 shared
Perhaps most telling are the donor contamination levels s d , which came out as follows: Note that in several of the tumor sections, the fitted model suggests that the donor contamination levels are very high, approaching the assumed upper limit of 0.2. In fact, if the prior distributions had not been constrained by the upper limit of 0.2, the Markov chain would have resorted to even higher to levels of contamination that are much too high to be plausible. Contamination from donor

Model comparison
To compare the fits of the contamination and fusion models, a quick first indication was obtained by inspecting the deviances for each model.
The deviances for the fusion model were clearly smaller than those for the contamination model, indicating a better fit for fusion. In view of the fact that the fusion model has fewer parameters (6 more allele count parameters but 9 fewer contamination parameters) than the contamination model, which is expected to put the fusion model at a disadvantage as far as deviances are concerned, this comparison is all the more striking.
For a probabilistic comparison we turned to the log pseudo-marginal likelihood (LPML, (6)), a measure of model fit advocated in the statistical literature (1,2). We calculated the LPML for both the fusion model and contamination model as fit to our observed data. These two individual values are not particularly meaningful on their own, but the difference (also known as the log pseudo-Bayes factor) is of interest, indicating how much better the fusion model fit our data than the contamination model did. An important advantage of this approach over those based on standard Bayes factors is that the quantities we are computing are much less sensitive to the choice of prior distributions. For our data, the LPML difference turned out to be 71.4, the positive value indicating that the fusion model fit the data better than the contamination model. To assess the statistical significance of the value 71.4, we used a computationally intensive calibration procedure (7,8), in which 400 random data sets were simulated under the two models, and for each simulated data set, an LPML difference was calculated. The calibration distributions obtained by this procedure are shown in the histograms in Fig. S9, where the red lines show the calculated value 71.4 of this LPML difference for our data. As shown in Fig. S9, under contamination, all 400 of the LPML differences were less than 71.4, leading to an empirical two-sided P value bounded by 2 0.005 400 P < = . Thus, LPML differences as high as 71.4 are very rare under the contamination model. In contrast, under the fusion model, a LPML difference of 71.4 was quite typical, being at the 18.5 percentile of the calibration distribution, leading to a P value of 0.37. The finding of a small P value for contamination supports the assertion that the contamination model fails to explain our data. In contrast, the much larger P value for fusion indicates that our data is consistent with the fusion model.

Model variations
A number of variations of the above models were considered and evaluated by the same methods. As mentioned above, we tried varying the prior distributions for allele counts in the cancer cells from the distribution p1 to the distribution p2 defined in Table S2. Compared to p1, the distribution p2 places more probability on 1 copy and less probability on losses and gains, particularly the higher copy numbers. But the prior p2 led to the same conclusions, giving a P value less than 0.005 for contamination and P=0.645 for fusion. Another modification was to replace the Normal error distributions by t distributions, which have longer tails and allow more extreme outliers. We also investigated a simple form of tumor evolution by extending the above models to allow repeat numbers within a single locus to take two different values over the different tumor sections. None of these more complicated models was found to provide a significant improvement over the final models presented above in fitting our data.