Statistical inference of transmission fidelity of DNA methylation patterns over somatic cell divisions in mammals

We develop Bayesian inference methods for a recently-emerging type of epigenetic data to study the transmission fidelity of DNA methylation patterns over cell divisions. The data consist of parent-daughter double-stranded DNA methylation patterns with each pattern coming from a single cell and represented as an unordered pair of binary strings. The data are technically difficult and time-consuming to collect, putting a premium on an efficient inference method. Our aim is to estimate rates for the maintenance and de novo methylation events that gave rise to the observed patterns, while accounting for measurement error. We model data at multiple sites jointly, thus using whole-strand information, and considerably reduce confounding between parameters. We also adopt a hierarchical structure that allows for variation in rates across sites without an explosion in the effective number of parameters. Our context-specific priors capture the expected stationarity, or near-stationarity, of the stochastic process that generated the data analyzed here. This expected stationarity is shown to greatly increase the precision of the estimation. Applying our model to a data set collected at the human FMR1 locus, we find that measurement errors, generally ignored in similar studies, occur at a nontrivial rate (inappropriate bisulfite conversion error: 1.6$$ with 80$$ CI: 0.9--2.3$$). Accounting for these errors has a substantial impact on estimates of key biological parameters. The estimated average failure of maintenance rate and daughter de novo rate decline from 0.04 to 0.024 and from 0.14 to 0.07, respectively, when errors are accounted for. Our results also provide evidence that de novo events may occur on both parent and daughter strands: the median parent and daughter de novo rates are 0.08 (80$$ CI: 0.04--0.13) and 0.07 (80$$ CI: 0.04--0.11), respectively.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS297 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evaluating an unconfined aquifer by analysis of age-dating tracers in stream water

The mean transit time (MTT) is a fundamental property of a groundwater flow system that is strongly related to the ratio of recharge rate to storage volume. However, obtaining samples for estimating the MTT using environmental tracers is problematic as flow-weighted samples over the full spectrum of transit times are needed. Samples collected fromthe base flow of a gaining stream in the North Carolina Coastal Plain (West Bear Creek) that were corrected for exchange with the atmosphere yielded environmental tracer concentrations (SF6 and CFC-11) very similar to flow-weighted values from nine or ten streambed piezometers that directly sampled groundwater during low streamflow. At higher streamflow on the falling limb of the hydrograph, stream tracer concentrations (after correction for gas exchange) were significantly higher than the flow-weighted mean from piezometers, consistent with dominance of the streamtracer signal by transient influx of surface water and/or younger subsurface water. The apparent MTT derived from SF6 in low flow stream water samples was 26 years, suggesting a groundwater recharge rate of about 210 mm/yr, that is consistent with vertical profiles obtained by sampling nested piezometers in the aquifer. When sampled under low flow conditions when streamflow consists of a high component of groundwater discharge, West Bear Creek appears to act as a flow-weighted integrator of transit times and, streamflow samples can provide fundamental information regarding groundwater recharge rate and MTT. Our study suggests that watershed-scale evaluation of some groundwater flow systems is possible without utilizing monitoring wells

Groundwater transit time distribution and mean from streambed sampling in an agricultural coastal plain watershed, North Carolina, USA

We measured groundwater apparent age (s) and seepage rate (v) in a sandy streambed using point-scale sampling and seepage blankets (a novel seepage meter). We found very similar MTT estimates from streambed point sampling in a 58 m reach (29 years) and a 2.5 km reach (31 years). The TTD for groundwater discharging to the stream was best fit by a gamma distribution model and was very similar for streambed point sampling in both reaches. Between adjacent point-scale and seepage blanket samples, water from the seepage blankets was generally younger, largely because blanket samples contained a fraction of ‘‘young’’ stream water. Correcting blanket data for the stream water fraction brought s estimates for most blanket samples closer to those for adjacent point samples. The MTT estimates from corrected blanket data were in good agreement with those from sampling streambed points adjacent to the blankets. Collectively, agreement among age-dating tracers, general accord between tracer data and piston-flow model curves, and large groundwater age gradients in the streambed, suggested that the piston flow apparent ages were reasonable estimates of the groundwater transit times for most samples. Overall, our results from two field campaigns suggest that groundwater collected in the streambed can provide reasonable estimates of apparent age of groundwater discharge, and that MTT can be determined from different agedating tracers and by sampling with different groundwater collection devices. Coupled streambed point measurements of groundwater age and groundwater seepage rate represent a novel, reproducible, and effective approach to estimating aquifer TTD and MTT

Quantifying the fate of agricultural nitrogen in an unconfined aquifer: Stream-based observations at three measurement scales

We compared three stream-based sampling methods to study the fate of nitrate in groundwater in a coastal plain watershed: point measurements beneath the streambed, seepage blankets (novel seepage-meter design), and reach mass-balance. The methods gave similar mean groundwater seepage rates into the stream (0.3–0.6 m/d) during two 3–4 day field campaigns despite an order of magnitude difference in stream discharge between the campaigns. At low flow, estimates of flowweighted mean nitrate concentrations in groundwater discharge ([NO-3 ]FWM) and nitrate flux from groundwater to the stream decreased with increasing degree of channel influence and measurement scale, i.e., [NO-3 ]FWM was 654, 561, and 451 mM for point, blanket, and reach mass-balance sampling, respectively. At high flow the trend was reversed, likely because reach mass-balance captured inputs from shallow transient high-nitrate flow paths while point and blanket measurements did not. Point sampling may be better suited to estimating aquifer discharge of nitrate, while reach mass-balance reflects full nitrate inputs into the channel (which at high flow may be more than aquifer discharge due to transient flow paths, and at low flow may be less than aquifer discharge due to channel-based nitrate removal). Modeling dissolved N2 from streambed samples suggested (1) about half of groundwater nitrate was denitrified prior to discharge from the aquifer, and (2) both extent of denitrification and initial nitrate concentration in groundwater (700–1300 mM) were related to land use, suggesting these forms of streambed sampling for groundwater can reveal watershed spatial relations relevant to nitrate contamination and fate in the aquifer

Errors in the bisulfite conversion of DNA: modulating inappropriate- and failed-conversion frequencies

Bisulfite treatment can be used to ascertain the methylation states of individual cytosines in DNA. Ideally, bisulfite treatment deaminates unmethylated cytosines to uracils, and leaves 5-methylcytosines unchanged. Two types of bisulfite-conversion error occur: inappropriate conversion of 5-methylcytosine to thymine, and failure to convert unmethylated cytosine to uracil. Conventional bisulfite treatment requires hours of exposure to low-molarity, low-temperature bisulfite (‘LowMT’) and, sometimes, thermal denaturation. An alternate, high-molarity, high-temperature (‘HighMT’) protocol has been reported to accelerate conversion and to reduce inappropriate conversion. We used molecular encoding to obtain validated, individual-molecule data on failed- and inappropriate-conversion frequencies for LowMT and HighMT treatments of both single-stranded and hairpin-linked oligonucleotides. After accounting for bisulfite-independent error, we found that: (i) inappropriate-conversion events accrue predominantly on molecules exposed to bisulfite after they have attained complete or near-complete conversion; (ii) the HighMT treatment is preferable because it yields greater homogeneity among sites and among molecules in conversion rates, and thus yields more reliable data; (iii) different durations of bisulfite treatment will yield data appropriate to address different experimental questions; and (iv) conversion errors can be used to assess the validity of methylation data collected without the benefit of molecular encoding

Statistical Inference of In Vivo Properties of Human DNA Methyltransferases from Double-Stranded Methylation Patterns

DNA methyltransferases establish methylation patterns in cells and transmit these patterns over cell generations, thereby influencing each cell's epigenetic states. Three primary DNA methyltransferases have been identified in mammals: DNMT1, DNMT3A and DNMT3B. Extensive in vitro studies have investigated key properties of these enzymes, namely their substrate specificity and processivity. Here we study these properties in vivo, by applying novel statistical analysis methods to double-stranded DNA methylation patterns collected using hairpin-bisulfite PCR. Our analysis fits a novel Hidden Markov Model (HMM) to the observed data, allowing for potential bisulfite conversion errors, and yields statistical estimates of parameters that quantify enzyme processivity and substrate specificity. We apply this model to methylation patterns established in vivo at three loci in humans: two densely methylated inactive X (Xi)-linked loci ( and ), and an autosomal locus (), where methylation densities are tissue-specific but moderate. We find strong evidence for a high level of processivity of DNMT1 at and , with the mean association tract length being a few hundred base pairs. Regardless of tissue types, methylation patterns at are dominated by DNMT1 maintenance events, similar to the two Xi-linked loci, but are insufficiently informative regarding processivity to draw any conclusions about processivity at that locus. At all three loci we find that DNMT1 shows a strong preference for adding methyl groups to hemi-methylated CpG sites over unmethylated sites. The data at all three loci also suggest low (possibly 0) association of the de novo methyltransferases, the DNMT3s, and are consequently uninformative about processivity or preference of these enzymes. We also extend our HMM to reanalyze published data on mouse DNMT1 activities in vitro. The results suggest shorter association tracts (and hence weaker processivity), and much longer non-association tracts than human DNMT1 in vivo

Testing the FMR1 Promoter for Mosaicism in DNA Methylation among CpG Sites, Strands, and Cells in FMR1-Expressing Males with Fragile X Syndrome

Variability among individuals in the severity of fragile X syndrome (FXS) is influenced by epigenetic methylation mosaicism, which may also be common in other complex disorders. The epigenetic signal of dense promoter DNA methylation is usually associated with gene silencing, as was initially reported for FMR1 alleles in individuals with FXS. A paradox arose when significant levels of FMR1 mRNA were reported for some males with FXS who had been reported to have predominately methylated alleles. We have used hairpin-bisufite PCR, validated with molecular batch-stamps and barcodes, to collect and assess double-stranded DNA methylation patterns from these previously studied males. These patterns enable us to distinguish among three possible forms of methylation mosaicism, any one of which could explain FMR1 expression in these males. Our data indicate that cryptic inter-cell mosaicism in DNA methylation can account for the presence of FMR1 mRNA in some individuals with FXS