BACKGROUND
studies of de novo mutation offer new potential to elucidate the etiology of both mendelian and complex human diseases  <cit> , made increasingly possible by efficient, large-scale re-sequencing of the coding portion of the human genome.
this class of mutations can lead to the identification of disease-causal genes  and etiological pathways  <cit> , help to refine the underlying genetic mechanism and architecture  <cit> , and ultimately can aid in clinical management of disease for mutational carriers.
after a causal gene has been identified, it is natural to hypothesize that disease relevant mutations accumulate within a sub-sequence of the gene – for example, an exon, a protein domain  <cit> , or at cpg sites  <cit> .
previous studies of de novo mutational burden for complex disease have largely focused on gene or pathway discovery, and have benefited from statistical models that capture base-pair variability in the mutation rate  <cit> .
however, because hundreds of genes are implicated for an individual complex disease, and owing to sizes of these studies which typically number in the hundreds to a few thousands subjects  <cit> , the number of de novo events per gene is small and thus limits the power to infer pathogenicity of sub-sequences within the gene.
in contrast, for mendelian diseases that are not extremely rare and where the genetic architecture is less complex , de novo mutational burden concentrates to individual genes  <cit> , facilitating the possibility of genic sub-sequence characterization.
however, previous efforts have largely been enumerative rather than quantitative, as improved models of mutation for the human genome  <cit>  and a large-scale collection of genetic variation segregating in the coding genomes of human populations have only been recently described  <cit> .
progress in investigating hypotheses of mutational burden within sub-sequences has been hampered by the lack of accurate models that capture mutation rate variability in human genomes at base-pair resolution.
previous studies have utilized approaches based on enrichment of de novo mutations in disease ascertained samples to infer pathogenicity .
however, because sub-genic sequences can introduce germline mutations more frequently due to a higher intrinsic rate of mutation, it is critical to model variation in mutation rate to accurately detect enrichment at sub-sequences  <cit> .
recently, we described a statistical model for nucleotide substitution using local sequence context, which explains a substantial fraction of variability in mutation rates observed in human populations  <cit> .
in what follows below, we describe an approach that facilitates direct hypothesis testing for an enrichment of de novo mutations within the sub-sequence of a gene, beyond that expected from our mutational model at base-pair resolution.
our report here differs from important, recent work demonstrating the functional intolerance to new mutations found in the protein domains of genes  <cit> , with application targeted toward variant prioritization for locus discovery in human disease.
in addition, our approach differs from existing tools like tada or poisson models  <cit> , which are designed to assess the total mutational burden in a gene.
in contrast, our approach directly tests for the enrichment of de novo mutations in disease ascertained samples over part of gene suspected to harbor pathogenicity  against a null hypothesis reflecting the background variable rate of mutation across a gene.
our objective is to assess if the distribution of mutations already observed is itself unusual, heterogeneous in space across a gene or within a mutational class.
as a proof of concept, we apply our testing framework on a data set consisting of de novo mutations discovered in  <dig> newly re-sequenced patients affected with sporadic, bilateral retinoblastoma .
rb is an extensively studied cancer of the developing retina, and the distinctive clinical features of bilateral tumors and a younger age at diagnosis is associated with the presence of germline mutations in the tumor suppressor retinoblastoma  <dig>  gene  <cit> .
in rb, it is not fully understood if de novo mutations occur uniformly over rb <dig>  or instead localize to specific codons, sequence contexts, or protein domains.
based on knudson’s model  <cit> , we expect a higher frequency of de novo mutations that result in putative loss-of function  in rb <dig> in patients ascertained for rb, which has been previously shown  <cit> .
numerous studies have reported a preponderance of nonsense mutations at cpg sites in rb <dig>  <cit> .
these observations could suggest a role of cpg sites in generating nonsense mutations via the deamination of hyper-methylated cpgs as a potential mechanism  <cit> , though this postulation remains to be statistically evaluated.
in addition, numerous splice-site mutations have also been observed in rb <dig>  <cit> , many of which have been shown to result in exon skipping  <cit> .
however, it remains to be quantified if mutations in all essential splice sites are equivalently pathogenic.
finally, recurrent point mutations have been observed at specific codons, which includes arg661trp .
this codon falls within the pocket domain in rb <dig>  <cit> , an important domain that facilitates binding of the protein product with downstream targets to regulate cell cycle.
however, to our knowledge, enrichment of mutations at this or other codons in rb <dig> has not been statistically quantified.
in what follows, we demonstrate  that the previously reported excess of nonsense mutations in rb <dig> at cpgs is compatible with the elevated rate of mutation at those sites, refuting a specific pathogenic mechanism in rb,  an enrichment of essential splice-site donor mutations at exon  <dig> and  <dig>  but depletion at exon  <dig>  indicative of previously unappreciated heterogeneity in relative penetrance across this type of putative lof mutation, and  a statistically significant excess of mutations found at arg661trp in bilateral rb, as a hotspot for missense mutations with lower penetrance.
our approach is generalizable across disease endpoints, providing a statistical framework to characterize rare diseases with today’s data, but also expanded, complex disease studies collected in the future.
RESULTS
an algorithm to quantify the enrichment of de novo mutations
our central objective is to determine if the frequency, type, and location of de novo mutations for a given gene are consistent with the number of events predicted from our local, nucleotide sequence context model for mutation rate variability.
for example, we expect more nonsense mutations in rb patients than our background model predicts, because  we ascertained individuals with rb,  nonsense mutations are likely lof, and  lof at rb <dig> causes rb.
to achieve this objective, we require an accurate model that captures variability in the frequency of de novo mutational events across a gene and an engine to distribute mutations in that gene according to this model.
with these in place, we can empirically assess significance of enrichment of de novo mutations in exons or sub-sequences of rb <dig> relative to our model prediction.
in our previous work  <cit>  we demonstrated that an expanded sequence context model which considers three flanking nucleotides on either side of a base , explains variation in germline mutation rate better than competing models of sequence context, and up to 93% of the variability in substitution probabilities.
using the sequence context based substitution probabilities, we developed an algorithm to distribute mutations across the gene in order to generate an expected count of mutations  at all positions in rb <dig> .
with these distributions in hand, we can estimate the empirical significance conditioned on the observed number of any type of substitution in any sub-sequence within the gene.
as an imperfect control, we use singletons from exac  in which to compare our de novo events, with the assumption that these events are the youngest and have not experienced the full force of purifying selection; i.e., are the closest proxy to de novo events segregating in  european populations.
in what follows, we apply our approach to study  the overall frequency of nonsense, essential splice-site, and missense mutations in rb <dig> and exac, and  their spatial occurrence by exon or by sub-sequence .fig.
<dig> approach to quantify if patterns of de novo within a mutational class are unusual.
our approach involves three steps.
first, we identify the genomic target  in which mutations will be characterized, and the total number of mutations found in that territory.
we then distribute this total number of mutations over the target territory using a background model of mutation rate.
second, we find the expected number of mutations in different categories  using the previous distribution samples.
third and finally, we compare this to the observed number of mutation to detect statistical enrichment in a category beyond expectation.
in this toy example depicted here, we focus on the genomic territory that can generate nonsense mutation , and imagine that we have identified  <dig> de novo mutations that are nonsense.
first, we identify eligible base pairs and that can result in a nonsense change.
next, we calculate the probability of mutation at each eligible base pair as the sum of substitution probabilities of that sequence context changing to a stop codon .
second, we then distribute the mutations over multiple simulations from a multinomial distribution, and find the distribution of the expected number of mutations at each of these eligible base pairs.
we are particularly interested in cases where the observed number of mutations at a subclass  is greater than what we see in simulations, as this is compatible with disease-relevant pathogenicity for this class of mutation, or position where the mutation is located.
third and finally, for a particular subclass we combine the expected mutations at different eligible base pairs and compare the overall expected distribution with observed, and conclude enrichment
re-sequencing of sporadic bilateral rb patients identifies  <dig> de novo single base point mutations
to quantify the role of de novo mutations in the pathophysiology in rb, we re-sequenced rb <dig> in  <dig> cases presenting sporadic , bilateral rb and their parents.
our targeted resequencing included all exons of rb <dig> as well as  <dig> base pairs of intronic sequences on either side of exons .
for statistical modeling purposes, we focused on single base point mutations and excluded individuals who carry a frame-shift or in-frame insertion-deletion mutations.
after variant calling followed by quality control, we identified  <dig> de novo germline, single base point mutations .
owing to an alternative start codon in exon  <dig>  <cit> , our subsequent analyses focus on the remaining exons, resulting in  <dig> amino-acid altering mutations,  <dig> in essential splice-sites, and  <dig> mutations found in introns outside of essential splice-sites .
consistent with the causal role of rb <dig>  the discovery of  <dig> de novo mutations in  <dig> rb probands is highly unusual .
furthermore, we observed more nonsense and essential splice-site mutations than missense or intronic mutations, expected given the pathogenic nature of loss-of-function  mutations in rb <dig> .
for a population-level comparison, we contrasted our mutational profile to the data obtained from the exome aggregation consortium   <cit> , consisting  <dig>  individuals re-sequenced for the exome.
we note that exac excluded childhood diseases from their aggregation, which may have excluded rb patients.
as a result, we do not expect this sample to represent a completely random population sampling of mutations in rb <dig>  from exac, we focused on singletons observed in non-finnish populations of european ancestry .
consistent with samples from exac as population-level controls with potential ascertainment against rb disease, we observed fewer loss-of function and more missense and intronic variants compared to our de novo mutations identified in rb probands .table  <dig> counts of de novo mutations in rb <dig> ascertained from rb patients, and singleton variants identified in exac from  europeans for various subtypes
abundance of nonsense mutation at cpg sites is explained by elevated mutation rate
we first investigated if nonsense mutations were distributed proportionally to the predicted rate of mutation, or alternatively localize to specific sequences, like cpgs.
as a positive control, we first distributed the  <dig> identified mutations ascertained in rb probands and determined how many nonsense mutations we predicted from our sequence context mutational model.
we found an enrichment of nonsense mutations beyond that expected from our model .
this observation is consistent with extensive literature showing that lof mutations at rb <dig> cause rb.
as a negative control, we distributed variants identified from the exac database, and observed fewer nonsense mutations than expected based on our model .
this is also expected, as we anticipate few  nonsense mutations in rb <dig> observed in the general population or in exac that may have excluded rb patients.fig.
<dig> overall and exon specific pathogenicity in nonsense mutations.
a comparison of the overall observed number of mutations to the simulated frequency of nonsense mutations in both rb and exac datasets.
b comparison of the observed number of mutations to the simulated frequency of nonsense mutations in rb, across exons  <dig> to  <dig>  the asterisk  denotes that the observed number falls outside the 99% confidence interval .
ci: confidence interval
we next examined if the subset of  <dig> nonsense mutations we observed were unusually distributed across exons in rb <dig> .
we found that, across virtually all exons, nonsense mutations occurred as frequently as our model predicts, broadly consistent with the concept that nonsense mutations found across rb <dig> are similarly pathogenic .
the single exception was exon  <dig>  which segregated fewer mutations than our model predicted .
this observation is compatible with the hypothesis that nonsense mutations in exon  <dig> are not fully penetrant, perhaps due to incomplete nonsense mediated decay  <cit>  or that this exon may not be integral to the etiology of rb.
previous studies have observed fewer mutations at later exons in the rb <dig> gene  <cit> , though they were unable to quantify the reduction and assess statistical significance as we are able to here.
while we observed fewer mutations at exons  <dig> and  <dig>  these numbers are still compatible with our background mutational model, given the number of mutations that were discovered in re-sequencing.
next, we examined if the subset of  <dig> nonsense mutations we observed were unusually distributed in amino acid type or codon contexts across rb <dig> .
we found that the distribution of de novo events by amino acid and codon context was not especially different from what our mutational model predicted .
specifically, our model predicted a large number of c-to-t transitions resulting in arginine to stop mutations at the cga codons , presumably due to the higher mutational frequency at the cpg context  <cit> .
this analysis indicates that the observed profile of nonsense mutations can be explained by the background rate of mutation without a need to invoke a rb-specific mutation-promoting or pathogenic mechanism at cpg sites.table  <dig> comparison of the observed number of nonsense de novo mutations to the simulated frequency predicted by our sequence context model
data shown for all amino acids which can change to a stop codon as well as arginine codon partitioned by cpg context.
ci confidence interval
to replicate these observations, we repeated our analysis on an independent set of  <dig> nonsense de novo germline mutations in rb <dig> identified in bilateral rb patients .
these results recapitulated the observed deficiency of nonsense events in exon  <dig>  and our model also matched the number of nonsense mutations at cpg sites or at cga codons relative to other nonsense sites .
excess splice-site donor mutations in introns  <dig> and  <dig>  but depleted in intron  <dig> of rb1
we next investigated if essential splice-site and intronic mutations were distributed proportionally to the rate of substitution predicted by our context model.
as a positive control, we distributed the  <dig> mutations ascertained in rb probands and determined how many essential splice-site and intronic mutations we expected from our sequence context mutational model.
we found more de novo essential splice sites mutations in rb patients than predicted .
this observation is consistent with the idea that essential splice-site mutations that are lof at rb <dig> cause rb.
as a negative control, we distributed variants identified from the exac database and observed fewer essential splice variants there .
this is not unexpected: analogous to nonsense mutations described above, we anticipate few essential splice-site mutations in the general population and/or ascertainment against rb patients in exac participants.
in intronic sequences that are found outside of essential splice sites, we observed substantially fewer events in rb patients that our model predicted .
in contrast, we found more intronic events in exac that our model would predict .
taken collectively, these two observations indicate that intronic and essential splice-site sequences do not have a homogeneous rate of mutational ascertainment, and given that intronic mutations are ascertained less frequently, indicate lower overall pathogenicity for intronic mutations outside of essential splice-sites , as expected given that essential splice sites are generally intolerant to mutation.fig.
<dig> overall and exon specific enrichment in essential splice-site mutations.
a comparison of the overall observed number of mutations to the simulated frequency of essential splice and intronic mutations in both rb and exac datasets.
b comparison of the observed number of mutations to the simulated frequency of essential splice donor mutations in rb, across exons  <dig> to  <dig>  the asterisk  denotes that the observed number falls outside the 99% confidence interval .
ci: confidence interval
we then examined if the  <dig> essential splice-site mutations we ascertained in rb probands were unusually distributed across introns in rb <dig> .
first, we found that essential splice-site acceptor mutations were not unusually distributed , so we focused on the remaining  <dig> essential splice-site donor mutations.
next, we observed no mutations in the donor site of intron  <dig>  which was outside our model prediction .
however, this observation is readily explainable: if we assume that essential splice-site donor mutations here result in exon skipping as seen for other splice-site mutations  <cit> , it turns out that skipping exon  <dig> retains the coding reading frame albeit with a  <dig> amino acid deletion .
therefore, this type of mutation may not result in full lof of the rb <dig> protein product, and thus, may be weakly penetrant, if at all.
next, we found that essential donor splice-site mutations in intron  <dig> and  <dig> segregated more mutations that our model predicted .
previous studies have observed that exon  <dig> and  <dig> mutations are recurrently mutated in rb <dig>  <cit> , though they were unable to quantify the enrichment and assess statistical significance as we are able to here.
it is not immediately apparent why these specific splice-site mutations are enriched in rb ascertained patients compared to other splice donor mutations.
essential donor splice-site mutations at intron  <dig> and  <dig> result in exon skipping  <cit> , out-of frame shift mutation, and putative lof .
however, essential donor splice-site mutations at other introns  also result in frame-shift mutations in rb <dig> if exons are skipped.
to further validate the observation of specific enrichment at these exons, we utilized the leiden open variation  database  <cit>  , a curated catalog of mutations found in rb <dig>  because variants are reported from multiple studies, where the gene territory re-sequenced and total number of individuals ascertained is not completely documented, we are limited in our ability to statistically quantify variant enrichment in lovd as we can for our data.
we found recurrent mutations with multiple reported variants  even in the lovd  <cit>  database of all reported variants in rb <dig> gene of patients with rb .
moreover, the donor sequences of inton  <dig> and  <dig> also are similar to other canonical splice sequences found at other  exons.
taken collectively, these data suggest some additional pathogenic burden of these mutations relative to other essential splice-sites in rb <dig> table  <dig> comparison of the observed number of essential donor splice-site de novo mutations at exons  <dig>   <dig>  and  <dig> to the simulated frequency predicted by our sequence context model
“lovd count” denotes the point variants observed at this site in the lovd dataset.
in exon  <dig>  we list separately the simulated frequency for each mutational class type .
ci confidence interval
localized enrichment of missense mutations to arg661trp in rb1
we investigated if missense mutations were distributed proportionally to the rate of substitution predicted by our context model.
we distributed the observed  <dig> mutations across the gene, and found significantly fewer missense mutations than expected .
this observation is consistent with the model that missense mutations as a class generally are less penetrant for rb, contrasting against the substantially higher penetrance of lof nonsense or essential splice mutations.
in contrast, exac participants were not unusual in the distribution of missense variants observed relative to our model prediction .
taken collectively, these data suggest that, as a class, missense mutation in rb <dig> are less frequently pathogenic than nonsense variants and result in fewer mutations ascertained in rb probands.fig.
<dig> exon specific and localized enrichment of missense mutations in rb <dig>  a comparison of the overall observed number of mutations to the simulated frequency of missense mutations in both rb and exac datasets.
b comparison of the observed number of mutations to the simulated frequency of missense mutations in rb, across exons  <dig> to 27
the idea that missense mutations generally are less penetrant for rb <dig> still leaves open the possibility of heterogeneity in pathogenicity among sub-sequences of rb <dig>  for example, arg661trp is a frequently observed mutation found in families that segregate lower penetrance .
computational prediction tools like polyphen <dig>  <cit>  or evolutionary conservation based metrics  <cit>  are frequently used to rank missense variants categories of deleteriousness as a proxy for pathogenicity.
we applied polyphen <dig> to classify all missense mutations we identified, and found most of them to be damaging .
to further improve the resolution of these predictions, we applied our approach to identify a smaller, statistically credible subset of missense mutations implicated in rb pathogenicity.
to achieve this, we distributed all  <dig> missense mutations we ascertained in rb probands across rb <dig> to determine if these rates were proportional to our predicted mutational model .
we observed a significant enrichment of missense mutations in exon  <dig>  mapping to the known pocket domain in rb <dig> .
although the pocket domain in rb <dig> gene encompasses other exons  <cit>  , we did not observe a specific enrichment of missense mutations there .
we next distributed the missense mutations within the pocket domain territory in rb <dig> .
we observed an excess of missense mutation burden within exon  <dig> in pocket domain box b near codon  <dig> than predicted by our model .fig.
<dig> comparison of the observed number of mutation to the simulated frequency of missense mutations over codons in the pocket domain of rb <dig>  here, a sliding window of  <dig> amino acids on either side of the codon was considered.
dotted line denotes the gap in the pocket domain
we next sought to localize the signal of the missense mutational burden within exon  <dig>  we distributed all missense mutations we observed within exon  <dig> , and observed an enrichment of missense mutations from cgg to tgg coding for a change from arginine to tryptophan .
specifically, we found the previously observed recurrent mutation arg661trp  occurred more frequently that our model predicted .
we note the limited resolution of polyphen <dig>  as it also predicts other sites nearby as damaging .
to place this observation in context of other missense mutations documented in rb <dig>  we evaluated the frequency of n =  <dig> missense mutations in exon  <dig> to  <dig>  curated by the lovd repository.
there, the most frequently cataloged missense mutation was arg661trp , with the next most frequently listed as c712r , g137d , and t307i .
however, when reflected against exac, arg661trp was observed only once  and c712r was not observed at all, consistent with putative pathogenicity of both variants.
in contrast, g137d and t307i were far more frequent in exac , suggestive of very low rb penetrance for these events.
while the lovd ascertainment is certainly complex and precludes us from formally evaluating statistical significance, these data are consistent with the importance of arg661trp as pathogenic and a frequently mutated position.
quantification of relative rates of different classes of mutations found in rb1
finally, we sought to quantify – relative to nonsense mutations – the rates of various sub-types of de novo mutations we observed in rb <dig>  assuming the penetrance of nonsense mutation is nearly full, the idea here is that if a subtype of de novo mutation were as penetrant as nonsense mutations, we would expect to have ascertained that subtype as frequently as nonsense mutations, proportional to the mutability of the subtype.
we found that the rate of ascertainment of essential splice-site mutations was statistically lower than nonsense mutations , consistent with the lower penetrance of essential splice mutations due to some less pathogenic changes observed at the essential splice positions .
similarly, the rate of intronic and missense mutations relative to nonsense was substantially smaller .
finally, while the rates of missense mutations found in both pocket domain box a and b were less frequent relative to nonsense mutations, we noted that mutations localized to box b were more frequent compared to missense mutations overall or in box a .
together, these data suggest a mixture of penetrant missense mutations found across rb <dig>  elevated in penetrance for box a mutations, and further elevated in box b, the box that also contains codon  <dig> fig.
<dig> comparison of the relative rates of different types of de novo mutations, normalized to the rate of nonsense mutations.
plotted is the mean of the ratio of observed number of mutations over expected based on the computational model.
mutational categories that have a different rate from the nonsense category  are denoted by an asterisk .
ci: confidence interval
discussion and
CONCLUSIONS
a major challenge in de novo mutational studies of rare and complex disease is to not only identify new pathogenic mutations, but also to statistically quantitate the enrichment of specific types of pathogenic mutations within a gene, in order to improve the understanding of gene-specific disease etiology.
to address this question, we developed a generalized approach, based on local nucleotide sequence context, to model variability in mutational probabilities at base pair resolution.
our motivation was based on the need to statistically evaluate specific hypothesis about the relative abundance – and inference about pathogenicity – of de novo mutations identified in probands selected for bilateral rb without a previous family history of disease.
our approach provides a strategy to statistically interpret the enrichment of specific types and location where mutations occur in genes, important as the clinical community obtains large numbers of mutations from re-sequencing and may be tempted to speculate on apparent excesses in mutational frequency without comparing to what might be expected by chance.
while the mutational model utilized here is the best performing from those that are currently available  <cit> , we expect that these models will continue to improve over time.
our proposed approach is flexible and can accommodate future, improved models.
the interpretation of our findings were also clarified by contrasting our results against singleton variants identified in the largest aggregation of publicly available sequenced exomes from exac.
one caveat here is that we assumed that observed singleton mutations were close  proxies to the de novo mutation rate.
that study did observe fewer singletons than expected, suggesting the signature of recurrent mutation.
thus, while our estimates here may report fewer that the total number expected, we note that the size of rb <dig>  the magnitude of the recurrent mutational imprint, and simulations suggest only a small impact on our interpretation of exac variation.
our collection is both of qualitative and clinical importance.
first, this study of sporadic rb cases identified under a research protocol represents the single largest dataset of de novo mutations in the rb <dig> gene reported to date.
thus, it removes many uncertainties associated with other data sets where there are many sources of non-homogeneity including sample ascertainment and methods used for mutation detection.
moreover, the significance of identifying de novo mutations for affected probands includes not only clinical management decisions, but also risk of a second cancer in the future as well as having additional, affected offspring.
thus, investigating the pathogenicity of de novo mutations by this study is both mechanistically and clinically relevant.
in terms of clinical importance, our results imply that  splice site mutations at exon five are likely not pathogenic,  that exon  <dig> and  <dig> splice junction mutations are unusually pathogenic, and  missense mutations around the pocket domain are more pathologically significant.
the latter two cases may motivate further clinical monitoring or phenotypic follow-up studies to quantify future cancer risk for those specific mutations.
the analysis we present on these data helps to bring clarity to several outstanding questions in the field.
first, we show that the frequency of nonsense mutations at cpg sites is compatible with our background model for the known, elevated rate of mutation at these sites.
a parsimonious interpretation of this result is simply that nonsense mutations at cpg sites in rb <dig> are, in fact, not preferentially rb pathogenic.
instead, the abundance of arginine to stop mutations can simply be explained by  ascertainment of rb affected probands,  that lof at rb <dig> causes rb, and  the mutability of this sequence context  <cit> .
second, we identified heterogeneity in the frequency of essential donor splice-site mutations across rb <dig>  in particular, we found a depletion of essential donor splice site in intron  <dig>  explainable by the fact that exon  <dig> skipping retains the coding frame  and thus may only be weakly penetrant.
we also found more essential donor splice-sites of introns  <dig> and  <dig> than predicted by our model, which result in frame-shift and putative lof.
we note that essential donor splice-sites in other introns also result in frame-shift and putative lof.
thus, a mechanistic explanation as to why exon  <dig> and  <dig> skipping and consequent frame-shift lof would be specifically ascertained in our probands remains elusive.
nonetheless, statistical quantification of this specific enrichment, to our knowledge, has not been previously reported.
finally, we quantified the excess of missense mutations in exon  <dig>  localized specifically to arg661trp.
while we noted the recurrence of five mutations to this specific codon, as well as and enrichment in another lovd dataset, we were not able to distinguish the relative frequency of this mutation from the rate of nonsense owing to the small number of events we ascertained.
previous reports in the literature gives some indication that this mutation is indeed low penetrance , and our results are consistent with these reports.
with sufficient data and a specific, probabilistic model, it is conceivable to utilize our approach to derive posterior distributions for penetrance for this and other classes of mutations we observed.
such may be the focus of future work.
we focused here exclusively on the analysis of rb, owing to the systematic extent that this disease has been previously studied, the preponderance of existing data sets, and minimal genetic heterogeneity for the condition.
despite this, our efforts helped to clarify existing hypotheses in the field around mutational mechanisms for the gene and point to new areas to study for this already well-studied disease.
that said, our framework could be readily applied for interpreting the large collection of de novo events in additional monogenic or oligogenic  diseases.
or alternative, in the near future for complex disorders where genes have been identified and re-sequenced in a large number of patient populations and numerous de novo events have been catalogued.
while each disease endpoint will have particular biological mechanisms to elucidate, the model and approach we present should provide a statistical framework to identify sequence-based features that point to unknown mechanisms underlying human disease.
data access
patient samples
patients included in this study were recruited as part of a research protocol between  <dig> and  <dig> from pediatric oncology clinics within north america.
the de novo mutations presented here were identified from  <dig> children in the genetic diagnostic laboratory at the university of pennsylvania.
these samples represent bilateral rb cases without family history, and where both parental dna sample was available.
parental dna samples were tested for the mutations identified in the respective affected child to rule out familial cases, and to unambiguously establish the presence of de novo mutational events.
of the  <dig> sporadic bilateral cases identified previously  <cit> , only  <dig> samples overlap .
dna isolation and sequencing
the isolation of dna, pcr amplification of rb <dig> sequences, and sanger sequencing of amplified pcr products was performed as previously described  <cit> .
primer sequences used for amplification are available on request.
rb <dig> genic sequence region
we considered the genic sequence of rb <dig> with accession number l <dig> in the genbank database.
only exons  <dig> to  <dig> in rb <dig> were analyzed; exon  <dig> was excluded to match the design of a previous study, owing to cryptic start site in the gene  <cit> , though exon  <dig> mutations did not appear unusually distributed .
we also analyzed  <dig> base pairs on both 5′ and 3′ ends of the exon.
six base pairs on the 3′ end of the exon were defined as donor essential splice sites, while  <dig> base pairs on the 5′ end were defined as acceptor essential splice sites.
the remaining nucleotides, from position  <dig> to  <dig> on the 3′ end of the exon, and from  <dig> to  <dig> on the 5′ end of the exon were defined as intronic sites.
as a result, we analyzed a total of  <dig>  nucleotide bases in the gene, out of which  <dig>  were from protein coding region,  <dig>  intronic and remaining  <dig> belonging to essential splice sites.
we provide the entire annotated genomic territory .
rb mutational data
a total of  <dig> mutations were identified, which included  <dig> point mutations.
furthermore, we considered missense, nonsense, essential splice , and intronic mutations that falling in the rb <dig> sequence region defined per the above, that passed quality control.
we note that the apparent difference between the total number of individuals sequenced  and the number of mutations found in rb <dig>  is not dramatically different than previous reports  <cit> , perhaps suggesting additional pathogenic non-coding variation missed by our survey focused primarily on coding sequences.
as a result,  <dig> mutations falling in our region of interest were analyzed.
exac variants
we only considered the singleton variants  in the non-finnish european populations from the exac dataset.
we initially downloaded all variants in “ensg00000139687” gene id from exac, including only mutations that were observed once .
as a result, we analyzed  <dig> singleton variants falling in our region of interest as described above.
rb mutational data from collaborators
we independently received nonsense mutational data from a recent publication of germline de novo mutations in rb  <cit> .
we analyzed  <dig> variants from this dataset that were present in our region of interest as described above.
lovd variants
we queried the variants present in the  <dig> release of the leiden open variation database  for in the rb <dig> gene.
we only reported the results from the point mutations present in the database.

 studies of de novo mutation offer new potential to elucidate the etiology of both mendelian and complex human diseases, made increasingly possible by efficient, large-scale re-sequencing of the coding portion of the human genome. this class of mutations can lead to the identification of disease-causal genes and etiological pathways, help to refine the underlying genetic mechanism and architecture, and ultimately can aid in clinical management of disease for mutational carriers. after a causal gene has been identified, it is natural to hypothesize that disease relevant mutations accumulate within a sub-sequence of the gene – for example, an exon, a protein domain, or at cpg sites. previous studies of de novo mutational burden for complex disease have largely focused on gene or pathway discovery, and have benefited from statistical models that capture base-pair variability in the mutation rate. however, because hundreds of genes are implicated for an individual complex disease, and owing to sizes of these studies which typically number in the hundreds to a few thousands subjects, the number of de novo events per gene is small and thus limits the power to infer pathogenicity of sub-sequences within the gene. in contrast, for mendelian diseases that are not extremely rare and where the genetic architecture is less complex, de novo mutational burden concentrates to individual genes, facilitating the possibility of genic sub-sequence characterization. however, previous efforts have largely been enumerative rather than quantitative, as improved models of mutation for the human genome and a large-scale collection of genetic variation segregating in the coding genomes of human populations have only been recently described. progress in investigating hypotheses of mutational burden within sub-sequences has been hampered by the lack of accurate models that capture mutation rate variability in human genomes at base-pair resolution. previous studies have utilized approaches based on enrichment of de novo mutations in disease ascertained samples to infer pathogenicity. however, because sub-genic sequences can introduce germline mutations more frequently due to a higher intrinsic rate of mutation, it is critical to model variation in mutation rate to accurately detect enrichment at sub-sequences. recently, we described a statistical model for nucleotide substitution using local sequence context, which explains a substantial fraction of variability in mutation rates observed in human populations. in what follows below, we describe an approach that facilitates direct hypothesis testing for an enrichment of de novo mutations within the sub-sequence of a gene, beyond that expected from our mutational model at base-pair resolution. our report here differs from important, recent work demonstrating the functional intolerance to new mutations found in the protein domains of genes, with application targeted toward variant prioritization for locus discovery in human disease. in addition, our approach differs from existing tools like tada or poisson models, which are designed to assess the total mutational burden in a gene. in contrast, our approach directly tests for the enrichment of de novo mutations in disease ascertained samples over part of gene suspected to harbor pathogenicity against a null hypothesis reflecting the background variable rate of mutation across a gene. our objective is to assess if the distribution of mutations already observed is itself unusual, heterogeneous in space across a gene or within a mutational class. as a proof of concept, we apply our testing framework on a data set consisting of de novo mutations discovered in newly re-sequenced patients affected with sporadic, bilateral retinoblastoma. rb is an extensively studied cancer of the developing retina, and the distinctive clinical features of bilateral tumors and a younger age at diagnosis is associated with the presence of germline mutations in the tumor suppressor retinoblastoma gene. in rb, it is not fully understood if de novo mutations occur uniformly over rb or instead localize to specific codons, sequence contexts, or protein domains. based on knudson’s model, we expect a higher frequency of de novo mutations that result in putative loss-of function in rb in patients ascertained for rb, which has been previously shown. numerous studies have reported a preponderance of nonsense mutations at cpg sites in rb. these observations could suggest a role of cpg sites in generating nonsense mutations via the deamination of hyper-methylated cpgs as a potential mechanism, though this postulation remains to be statistically evaluated. in addition, numerous splice-site mutations have also been observed in rb, many of which have been shown to result in exon skipping. however, it remains to be quantified if mutations in all essential splice sites are equivalently pathogenic. finally, recurrent point mutations have been observed at specific codons, which includes arg661trp. this codon falls within the pocket domain in rb, an important domain that facilitates binding of the protein product with downstream targets to regulate cell cycle. however, to our knowledge, enrichment of mutations at this or other codons in rb has not been statistically quantified. in what follows, we demonstrate that the previously reported excess of nonsense mutations in rb at cpgs is compatible with the elevated rate of mutation at those sites, refuting a specific pathogenic mechanism in rb, an enrichment of essential splice-site donor mutations at exon and but depletion at exon indicative of previously unappreciated heterogeneity in relative penetrance across this type of putative lof mutation, and a statistically significant excess of mutations found at arg661trp in bilateral rb, as a hotspot for missense mutations with lower penetrance. our approach is generalizable across disease endpoints, providing a statistical framework to characterize rare diseases with today’s data, but also expanded, complex disease studies collected in the future.  an algorithm to quantify the enrichment of de novo mutations our central objective is to determine if the frequency, type, and location of de novo mutations for a given gene are consistent with the number of events predicted from our local, nucleotide sequence context model for mutation rate variability. for example, we expect more nonsense mutations in rb patients than our background model predicts, because we ascertained individuals with rb, nonsense mutations are likely lof, and lof at rb causes rb. to achieve this objective, we require an accurate model that captures variability in the frequency of de novo mutational events across a gene and an engine to distribute mutations in that gene according to this model. with these in place, we can empirically assess significance of enrichment of de novo mutations in exons or sub-sequences of rb relative to our model prediction. in our previous work we demonstrated that an expanded sequence context model which considers three flanking nucleotides on either side of a base, explains variation in germline mutation rate better than competing models of sequence context, and up to 93% of the variability in substitution probabilities. using the sequence context based substitution probabilities, we developed an algorithm to distribute mutations across the gene in order to generate an expected count of mutations at all positions in rb. with these distributions in hand, we can estimate the empirical significance conditioned on the observed number of any type of substitution in any sub-sequence within the gene. as an imperfect control, we use singletons from exac in which to compare our de novo events, with the assumption that these events are the youngest and have not experienced the full force of purifying selection; i.e., are the closest proxy to de novo events segregating in european populations. in what follows, we apply our approach to study the overall frequency of nonsense, essential splice-site, and missense mutations in rb and exac, and their spatial occurrence by exon or by sub-sequence.fig. approach to quantify if patterns of de novo within a mutational class are unusual. our approach involves three steps. first, we identify the genomic target in which mutations will be characterized, and the total number of mutations found in that territory. we then distribute this total number of mutations over the target territory using a background model of mutation rate. second, we find the expected number of mutations in different categories using the previous distribution samples. third and finally, we compare this to the observed number of mutation to detect statistical enrichment in a category beyond expectation. in this toy example depicted here, we focus on the genomic territory that can generate nonsense mutation, and imagine that we have identified de novo mutations that are nonsense. first, we identify eligible base pairs and that can result in a nonsense change. next, we calculate the probability of mutation at each eligible base pair as the sum of substitution probabilities of that sequence context changing to a stop codon. second, we then distribute the mutations over multiple simulations from a multinomial distribution, and find the distribution of the expected number of mutations at each of these eligible base pairs. we are particularly interested in cases where the observed number of mutations at a subclass is greater than what we see in simulations, as this is compatible with disease-relevant pathogenicity for this class of mutation, or position where the mutation is located. third and finally, for a particular subclass we combine the expected mutations at different eligible base pairs and compare the overall expected distribution with observed, and conclude enrichment re-sequencing of sporadic bilateral rb patients identifies de novo single base point mutations to quantify the role of de novo mutations in the pathophysiology in rb, we re-sequenced rb in cases presenting sporadic, bilateral rb and their parents. our targeted resequencing included all exons of rb as well as base pairs of intronic sequences on either side of exons. for statistical modeling purposes, we focused on single base point mutations and excluded individuals who carry a frame-shift or in-frame insertion-deletion mutations. after variant calling followed by quality control, we identified de novo germline, single base point mutations. owing to an alternative start codon in exon, our subsequent analyses focus on the remaining exons, resulting in amino-acid altering mutations, in essential splice-sites, and mutations found in introns outside of essential splice-sites. consistent with the causal role of rb the discovery of de novo mutations in rb probands is highly unusual. furthermore, we observed more nonsense and essential splice-site mutations than missense or intronic mutations, expected given the pathogenic nature of loss-of-function mutations in rb. for a population-level comparison, we contrasted our mutational profile to the data obtained from the exome aggregation consortium, consisting individuals re-sequenced for the exome. we note that exac excluded childhood diseases from their aggregation, which may have excluded rb patients. as a result, we do not expect this sample to represent a completely random population sampling of mutations in rb from exac, we focused on singletons observed in non-finnish populations of european ancestry. consistent with samples from exac as population-level controls with potential ascertainment against rb disease, we observed fewer loss-of function and more missense and intronic variants compared to our de novo mutations identified in rb probands.table counts of de novo mutations in rb ascertained from rb patients, and singleton variants identified in exac from europeans for various subtypes abundance of nonsense mutation at cpg sites is explained by elevated mutation rate we first investigated if nonsense mutations were distributed proportionally to the predicted rate of mutation, or alternatively localize to specific sequences, like cpgs. as a positive control, we first distributed the identified mutations ascertained in rb probands and determined how many nonsense mutations we predicted from our sequence context mutational model. we found an enrichment of nonsense mutations beyond that expected from our model. this observation is consistent with extensive literature showing that lof mutations at rb cause rb. as a negative control, we distributed variants identified from the exac database, and observed fewer nonsense mutations than expected based on our model. this is also expected, as we anticipate few nonsense mutations in rb observed in the general population or in exac that may have excluded rb patients.fig. overall and exon specific pathogenicity in nonsense mutations. a comparison of the overall observed number of mutations to the simulated frequency of nonsense mutations in both rb and exac datasets. b comparison of the observed number of mutations to the simulated frequency of nonsense mutations in rb, across exons to the asterisk denotes that the observed number falls outside the 99% confidence interval. ci: confidence interval we next examined if the subset of nonsense mutations we observed were unusually distributed across exons in rb. we found that, across virtually all exons, nonsense mutations occurred as frequently as our model predicts, broadly consistent with the concept that nonsense mutations found across rb are similarly pathogenic. the single exception was exon which segregated fewer mutations than our model predicted. this observation is compatible with the hypothesis that nonsense mutations in exon are not fully penetrant, perhaps due to incomplete nonsense mediated decay or that this exon may not be integral to the etiology of rb. previous studies have observed fewer mutations at later exons in the rb gene, though they were unable to quantify the reduction and assess statistical significance as we are able to here. while we observed fewer mutations at exons and these numbers are still compatible with our background mutational model, given the number of mutations that were discovered in re-sequencing. next, we examined if the subset of nonsense mutations we observed were unusually distributed in amino acid type or codon contexts across rb. we found that the distribution of de novo events by amino acid and codon context was not especially different from what our mutational model predicted. specifically, our model predicted a large number of c-to-t transitions resulting in arginine to stop mutations at the cga codons, presumably due to the higher mutational frequency at the cpg context. this analysis indicates that the observed profile of nonsense mutations can be explained by the background rate of mutation without a need to invoke a rb-specific mutation-promoting or pathogenic mechanism at cpg sites.table comparison of the observed number of nonsense de novo mutations to the simulated frequency predicted by our sequence context model data shown for all amino acids which can change to a stop codon as well as arginine codon partitioned by cpg context. ci confidence interval to replicate these observations, we repeated our analysis on an independent set of nonsense de novo germline mutations in rb identified in bilateral rb patients. these results recapitulated the observed deficiency of nonsense events in exon and our model also matched the number of nonsense mutations at cpg sites or at cga codons relative to other nonsense sites. excess splice-site donor mutations in introns and but depleted in intron of rb1 we next investigated if essential splice-site and intronic mutations were distributed proportionally to the rate of substitution predicted by our context model. as a positive control, we distributed the mutations ascertained in rb probands and determined how many essential splice-site and intronic mutations we expected from our sequence context mutational model. we found more de novo essential splice sites mutations in rb patients than predicted. this observation is consistent with the idea that essential splice-site mutations that are lof at rb cause rb. as a negative control, we distributed variants identified from the exac database and observed fewer essential splice variants there. this is not unexpected: analogous to nonsense mutations described above, we anticipate few essential splice-site mutations in the general population and/or ascertainment against rb patients in exac participants. in intronic sequences that are found outside of essential splice sites, we observed substantially fewer events in rb patients that our model predicted. in contrast, we found more intronic events in exac that our model would predict. taken collectively, these two observations indicate that intronic and essential splice-site sequences do not have a homogeneous rate of mutational ascertainment, and given that intronic mutations are ascertained less frequently, indicate lower overall pathogenicity for intronic mutations outside of essential splice-sites, as expected given that essential splice sites are generally intolerant to mutation.fig. overall and exon specific enrichment in essential splice-site mutations. a comparison of the overall observed number of mutations to the simulated frequency of essential splice and intronic mutations in both rb and exac datasets. b comparison of the observed number of mutations to the simulated frequency of essential splice donor mutations in rb, across exons to the asterisk denotes that the observed number falls outside the 99% confidence interval. ci: confidence interval we then examined if the essential splice-site mutations we ascertained in rb probands were unusually distributed across introns in rb. first, we found that essential splice-site acceptor mutations were not unusually distributed, so we focused on the remaining essential splice-site donor mutations. next, we observed no mutations in the donor site of intron which was outside our model prediction. however, this observation is readily explainable: if we assume that essential splice-site donor mutations here result in exon skipping as seen for other splice-site mutations, it turns out that skipping exon retains the coding reading frame albeit with a amino acid deletion. therefore, this type of mutation may not result in full lof of the rb protein product, and thus, may be weakly penetrant, if at all. next, we found that essential donor splice-site mutations in intron and segregated more mutations that our model predicted. previous studies have observed that exon and mutations are recurrently mutated in rb, though they were unable to quantify the enrichment and assess statistical significance as we are able to here. it is not immediately apparent why these specific splice-site mutations are enriched in rb ascertained patients compared to other splice donor mutations. essential donor splice-site mutations at intron and result in exon skipping, out-of frame shift mutation, and putative lof. however, essential donor splice-site mutations at other introns also result in frame-shift mutations in rb if exons are skipped. to further validate the observation of specific enrichment at these exons, we utilized the leiden open variation database, a curated catalog of mutations found in rb because variants are reported from multiple studies, where the gene territory re-sequenced and total number of individuals ascertained is not completely documented, we are limited in our ability to statistically quantify variant enrichment in lovd as we can for our data. we found recurrent mutations with multiple reported variants even in the lovd database of all reported variants in rb gene of patients with rb. moreover, the donor sequences of inton and also are similar to other canonical splice sequences found at other exons. taken collectively, these data suggest some additional pathogenic burden of these mutations relative to other essential splice-sites in rb table comparison of the observed number of essential donor splice-site de novo mutations at exons and to the simulated frequency predicted by our sequence context model “lovd count” denotes the point variants observed at this site in the lovd dataset. in exon we list separately the simulated frequency for each mutational class type. ci confidence interval localized enrichment of missense mutations to arg661trp in rb1 we investigated if missense mutations were distributed proportionally to the rate of substitution predicted by our context model. we distributed the observed mutations across the gene, and found significantly fewer missense mutations than expected. this observation is consistent with the model that missense mutations as a class generally are less penetrant for rb, contrasting against the substantially higher penetrance of lof nonsense or essential splice mutations. in contrast, exac participants were not unusual in the distribution of missense variants observed relative to our model prediction. taken collectively, these data suggest that, as a class, missense mutation in rb are less frequently pathogenic than nonsense variants and result in fewer mutations ascertained in rb probands.fig. exon specific and localized enrichment of missense mutations in rb a comparison of the overall observed number of mutations to the simulated frequency of missense mutations in both rb and exac datasets. b comparison of the observed number of mutations to the simulated frequency of missense mutations in rb, across exons to 27 the idea that missense mutations generally are less penetrant for rb still leaves open the possibility of heterogeneity in pathogenicity among sub-sequences of rb for example, arg661trp is a frequently observed mutation found in families that segregate lower penetrance. computational prediction tools like polyphen or evolutionary conservation based metrics are frequently used to rank missense variants categories of deleteriousness as a proxy for pathogenicity. we applied polyphen to classify all missense mutations we identified, and found most of them to be damaging. to further improve the resolution of these predictions, we applied our approach to identify a smaller, statistically credible subset of missense mutations implicated in rb pathogenicity. to achieve this, we distributed all missense mutations we ascertained in rb probands across rb to determine if these rates were proportional to our predicted mutational model. we observed a significant enrichment of missense mutations in exon mapping to the known pocket domain in rb. although the pocket domain in rb gene encompasses other exons, we did not observe a specific enrichment of missense mutations there. we next distributed the missense mutations within the pocket domain territory in rb. we observed an excess of missense mutation burden within exon in pocket domain box b near codon than predicted by our model.fig. comparison of the observed number of mutation to the simulated frequency of missense mutations over codons in the pocket domain of rb here, a sliding window of amino acids on either side of the codon was considered. dotted line denotes the gap in the pocket domain we next sought to localize the signal of the missense mutational burden within exon we distributed all missense mutations we observed within exon, and observed an enrichment of missense mutations from cgg to tgg coding for a change from arginine to tryptophan. specifically, we found the previously observed recurrent mutation arg661trp occurred more frequently that our model predicted. we note the limited resolution of polyphen as it also predicts other sites nearby as damaging. to place this observation in context of other missense mutations documented in rb we evaluated the frequency of n =  missense mutations in exon to curated by the lovd repository. there, the most frequently cataloged missense mutation was arg661trp, with the next most frequently listed as c712r, g137d, and t307i. however, when reflected against exac, arg661trp was observed only once and c712r was not observed at all, consistent with putative pathogenicity of both variants. in contrast, g137d and t307i were far more frequent in exac, suggestive of very low rb penetrance for these events. while the lovd ascertainment is certainly complex and precludes us from formally evaluating statistical significance, these data are consistent with the importance of arg661trp as pathogenic and a frequently mutated position. quantification of relative rates of different classes of mutations found in rb1 finally, we sought to quantify – relative to nonsense mutations – the rates of various sub-types of de novo mutations we observed in rb assuming the penetrance of nonsense mutation is nearly full, the idea here is that if a subtype of de novo mutation were as penetrant as nonsense mutations, we would expect to have ascertained that subtype as frequently as nonsense mutations, proportional to the mutability of the subtype. we found that the rate of ascertainment of essential splice-site mutations was statistically lower than nonsense mutations, consistent with the lower penetrance of essential splice mutations due to some less pathogenic changes observed at the essential splice positions. similarly, the rate of intronic and missense mutations relative to nonsense was substantially smaller. finally, while the rates of missense mutations found in both pocket domain box a and b were less frequent relative to nonsense mutations, we noted that mutations localized to box b were more frequent compared to missense mutations overall or in box a. together, these data suggest a mixture of penetrant missense mutations found across rb elevated in penetrance for box a mutations, and further elevated in box b, the box that also contains codon fig. comparison of the relative rates of different types of de novo mutations, normalized to the rate of nonsense mutations. plotted is the mean of the ratio of observed number of mutations over expected based on the computational model. mutational categories that have a different rate from the nonsense category are denoted by an asterisk. ci: confidence interval discussion and  a major challenge in de novo mutational studies of rare and complex disease is to not only identify new pathogenic mutations, but also to statistically quantitate the enrichment of specific types of pathogenic mutations within a gene, in order to improve the understanding of gene-specific disease etiology. to address this question, we developed a generalized approach, based on local nucleotide sequence context, to model variability in mutational probabilities at base pair resolution. our motivation was based on the need to statistically evaluate specific hypothesis about the relative abundance – and inference about pathogenicity – of de novo mutations identified in probands selected for bilateral rb without a previous family history of disease. our approach provides a strategy to statistically interpret the enrichment of specific types and location where mutations occur in genes, important as the clinical community obtains large numbers of mutations from re-sequencing and may be tempted to speculate on apparent excesses in mutational frequency without comparing to what might be expected by chance. while the mutational model utilized here is the best performing from those that are currently available, we expect that these models will continue to improve over time. our proposed approach is flexible and can accommodate future, improved models. the interpretation of our findings were also clarified by contrasting our results against singleton variants identified in the largest aggregation of publicly available sequenced exomes from exac. one caveat here is that we assumed that observed singleton mutations were close proxies to the de novo mutation rate. that study did observe fewer singletons than expected, suggesting the signature of recurrent mutation. thus, while our estimates here may report fewer that the total number expected, we note that the size of rb the magnitude of the recurrent mutational imprint, and simulations suggest only a small impact on our interpretation of exac variation. our collection is both of qualitative and clinical importance. first, this study of sporadic rb cases identified under a research protocol represents the single largest dataset of de novo mutations in the rb gene reported to date. thus, it removes many uncertainties associated with other data sets where there are many sources of non-homogeneity including sample ascertainment and methods used for mutation detection. moreover, the significance of identifying de novo mutations for affected probands includes not only clinical management decisions, but also risk of a second cancer in the future as well as having additional, affected offspring. thus, investigating the pathogenicity of de novo mutations by this study is both mechanistically and clinically relevant. in terms of clinical importance, our results imply that splice site mutations at exon five are likely not pathogenic, that exon and splice junction mutations are unusually pathogenic, and missense mutations around the pocket domain are more pathologically significant. the latter two cases may motivate further clinical monitoring or phenotypic follow-up studies to quantify future cancer risk for those specific mutations. the analysis we present on these data helps to bring clarity to several outstanding questions in the field. first, we show that the frequency of nonsense mutations at cpg sites is compatible with our background model for the known, elevated rate of mutation at these sites. a parsimonious interpretation of this result is simply that nonsense mutations at cpg sites in rb are, in fact, not preferentially rb pathogenic. instead, the abundance of arginine to stop mutations can simply be explained by ascertainment of rb affected probands, that lof at rb causes rb, and the mutability of this sequence context. second, we identified heterogeneity in the frequency of essential donor splice-site mutations across rb in particular, we found a depletion of essential donor splice site in intron explainable by the fact that exon skipping retains the coding frame and thus may only be weakly penetrant. we also found more essential donor splice-sites of introns and than predicted by our model, which result in frame-shift and putative lof. we note that essential donor splice-sites in other introns also result in frame-shift and putative lof. thus, a mechanistic explanation as to why exon and skipping and consequent frame-shift lof would be specifically ascertained in our probands remains elusive. nonetheless, statistical quantification of this specific enrichment, to our knowledge, has not been previously reported. finally, we quantified the excess of missense mutations in exon localized specifically to arg661trp. while we noted the recurrence of five mutations to this specific codon, as well as and enrichment in another lovd dataset, we were not able to distinguish the relative frequency of this mutation from the rate of nonsense owing to the small number of events we ascertained. previous reports in the literature gives some indication that this mutation is indeed low penetrance, and our results are consistent with these reports. with sufficient data and a specific, probabilistic model, it is conceivable to utilize our approach to derive posterior distributions for penetrance for this and other classes of mutations we observed. such may be the focus of future work. we focused here exclusively on the analysis of rb, owing to the systematic extent that this disease has been previously studied, the preponderance of existing data sets, and minimal genetic heterogeneity for the condition. despite this, our efforts helped to clarify existing hypotheses in the field around mutational mechanisms for the gene and point to new areas to study for this already well-studied disease. that said, our framework could be readily applied for interpreting the large collection of de novo events in additional monogenic or oligogenic diseases. or alternative, in the near future for complex disorders where genes have been identified and re-sequenced in a large number of patient populations and numerous de novo events have been catalogued. while each disease endpoint will have particular biological mechanisms to elucidate, the model and approach we present should provide a statistical framework to identify sequence-based features that point to unknown mechanisms underlying human disease. data access patient samples patients included in this study were recruited as part of a research protocol between and from pediatric oncology clinics within north america. the de novo mutations presented here were identified from children in the genetic diagnostic laboratory at the university of pennsylvania. these samples represent bilateral rb cases without family history, and where both parental dna sample was available. parental dna samples were tested for the mutations identified in the respective affected child to rule out familial cases, and to unambiguously establish the presence of de novo mutational events. of the sporadic bilateral cases identified previously, only samples overlap. dna isolation and sequencing the isolation of dna, pcr amplification of rb sequences, and sanger sequencing of amplified pcr products was performed as previously described. primer sequences used for amplification are available on request. rb genic sequence region we considered the genic sequence of rb with accession number l in the genbank database. only exons to in rb were analyzed; exon was excluded to match the design of a previous study, owing to cryptic start site in the gene, though exon mutations did not appear unusually distributed. we also analyzed base pairs on both 5′ and 3′ ends of the exon. six base pairs on the 3′ end of the exon were defined as donor essential splice sites, while base pairs on the 5′ end were defined as acceptor essential splice sites. the remaining nucleotides, from position to on the 3′ end of the exon, and from to on the 5′ end of the exon were defined as intronic sites. as a result, we analyzed a total of nucleotide bases in the gene, out of which were from protein coding region, intronic and remaining belonging to essential splice sites. we provide the entire annotated genomic territory. rb mutational data a total of mutations were identified, which included point mutations. furthermore, we considered missense, nonsense, essential splice, and intronic mutations that falling in the rb sequence region defined per the above, that passed quality control. we note that the apparent difference between the total number of individuals sequenced and the number of mutations found in rb is not dramatically different than previous reports, perhaps suggesting additional pathogenic non-coding variation missed by our survey focused primarily on coding sequences. as a result, mutations falling in our region of interest were analyzed. exac variants we only considered the singleton variants in the non-finnish european populations from the exac dataset. we initially downloaded all variants in “ensg00000139687” gene id from exac, including only mutations that were observed once. as a result, we analyzed singleton variants falling in our region of interest as described above. rb mutational data from collaborators we independently received nonsense mutational data from a recent publication of germline de novo mutations in rb. we analyzed variants from this dataset that were present in our region of interest as described above. lovd variants we queried the variants present in the release of the leiden open variation database for in the rb gene. we only reported the results from the point mutations present in the database. 
to address this issue, we present a generalized algorithm to grade the significance of de novo mutational burden within a gene ascertained from affected probands, based on our model for mutation rate informed by local sequence context. we confirm enrichment of loss-of-function mutations, but demonstrate that previously noted ‘hotspots’ of nonsense mutations in rb are compatible with the elevated mutation rates expected at cpg sites, refuting a rb specific pathogenic mechanism. mutation rateretinoblastomade novo mutationsvariability in mutation ratevariant prioritizationamerican heart association 13sdg14330006national institutes of health r01dk101478national institutes of health r01ca118580ganguly arupa http://dx.doi.org/ /100006108national center for advancing translational sciencesul1tr000003issue-copyright-statement© the author 2017 after a causal gene has been identified, it is natural to hypothesize that disease relevant mutations accumulate within a sub-sequence of the gene – for example, an exon, a protein domain, or at cpg sites. we applied our approach to newly identified de novo germline mutations by re-sequencing the coding exons and flanking intronic regions of rb in sporadic, bilateral probands affected with retinoblastoma. our approach is generalizable to any phenotype, and affirms the importance of statistical interpretation of de novo mutations found in human genomes. these assessments are typically qualitative, because we lack methodology to assess the statistical significance of sub-gene mutational burden ultimately to infer disease-relevant biology. we demonstrate the enrichment of missense mutations to the pocket domain of rb which contains the known arg661trp low-penetrance mutation. studies of de novo mutations offer great promise to improve our understanding of human disease.
 studies of de novo mutations offer great promise to improve our understanding of human disease. after a causal gene has been identified, it is natural to hypothesize that disease relevant mutations accumulate within a sub-sequence of the gene – for example, an exon, a protein domain, or at cpg sites. these assessments are typically qualitative, because we lack methodology to assess the statistical significance of sub-gene mutational burden ultimately to infer disease-relevant biology. methods to address this issue, we present a generalized algorithm to grade the significance of de novo mutational burden within a gene ascertained from affected probands, based on our model for mutation rate informed by local sequence context.  we applied our approach to newly identified de novo germline mutations by re-sequencing the coding exons and flanking intronic regions of rb in sporadic, bilateral probands affected with retinoblastoma. we confirm enrichment of loss-of-function mutations, but demonstrate that previously noted ‘hotspots’ of nonsense mutations in rb are compatible with the elevated mutation rates expected at cpg sites, refuting a rb specific pathogenic mechanism. our approach demonstrates an enrichment of splice-site donor mutations of exon and but depletion at exon indicative of previously unappreciated heterogeneity in penetrance within this class of substitution. we demonstrate the enrichment of missense mutations to the pocket domain of rb which contains the known arg661trp low-penetrance mutation.  our approach is generalizable to any phenotype, and affirms the importance of statistical interpretation of de novo mutations found in human genomes. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords mutation rateretinoblastomade novo mutationsvariability in mutation ratevariant prioritizationamerican heart association 13sdg14330006national institutes of health r01dk101478national institutes of health r01ca118580ganguly arupa http://dx.doi.org/ /100006108national center for advancing translational sciencesul1tr000003issue-copyright-statement© the author 2017 