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Parameter estimates under our HMM for the four human in vivo data sets.

<p>Medians and 80% credible intervals (CIs) of the posterior distribution of the parameters under our HMM are reported. The lower and upper limit of the 80% CI represent the 10- and 90-percentile, respectively. For hemi-preference ratios, one-sided 80% CIs are reported; that is, the lower limit is the 20-percentile of the distribution. Measurement error probability refers specifically to the inappropriate bisulfite conversion probability per CpG per strand (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#s4" target="_blank">Materials and Methods</a> for detail). Except for mean association lengths and hemi-preference ratios, estimates reported here were obtained under a uniform (0,1) prior. Entries with an are sensitive to the choice of the prior distribution; in other words, the data are less informative about these parameters.</p

Probabilities of measurement errors due to bisulfite conversion.

<p>True and observed methylation state of the parent-strand CpG in the -th double-strand methylation pattern at the -th site are denoted and , respectively. True and observed methylation states on the daughter-strand CpG are denoted and , respectively. Additionally, is the probability of failure of bisulfite conversion at a CpG, and the probability of inappropriate bisulfite conversion.</p

Estimated processivity and non-association tract lengths for human DNMT1 in vivo and mouse DNMT1 in vitro under our HMM.

<p>Each curve is the posterior distribution of the (<b>A</b>) mean association (processivity) and (<b>B</b>) non-association tract lengths on the scale. Vertical lines indicate the boundaries of the 80% CIs. Black curves indicate estimates from our in vivo human <i>FMR1</i> data. Magenta and green curves are based on our re-analysis of the in vitro mouse DNMT1 data in Goyal et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#pone.0032225-Goyal1" target="_blank">[11]</a> and Vilkaitis et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#pone.0032225-Vilkaitis1" target="_blank">[10]</a> (Supplementary Figure 12 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#pone.0032225.s001" target="_blank">Materials S1</a>).</p

Features of the three loci and summary statistics of the methylation patterns in the four human in vivo data sets.

*<p>Percentages of methylated, hemimethylated and unmethylated dyads.</p>**<p>Consecutive hemimethylated CpG dyads with methylated groups appearing on the same strand.</p

Four most informative <i>FMR1</i> methylation patterns and inference for each of them under HMM.

<p>Each pattern contains a pair of parent and daughter strands; which is the parent strand and which is the daughter strand is not known directly. Our HMM infers probabilistically the strand assignments for each pattern. These posterior probabilities are shown in green for the indicated parent and daughter strand assignment (indicated by letters P and D in green). These patterns from our <i>FMR1</i> data contain long runs of hemimethylated CpG dyads with their methyl groups present on the same strand. The top two most likely explanations, among all possible explanations, are shown for each pattern. Symbols indicate possible states and activities of the methyltransferases. Not all symbols are used here. The effect of these four patterns on parameter estimation is further shown in Supplementary Figure 13 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#pone.0032225.s001" target="_blank">Materials S1</a>.</p

Posterior distributions of dissociating probability from in vivo methylation data at several loci.

<p>From top to bottom, each row indicates for DNMT1 on the daughter strand, for the DNMT3s on the parent strand, and for the DNMT3s on the daughter strand. (<b>A1</b>)–(<b>A3</b>) are estimated for the locus. Estimates for , the other Xi-linked locus, show similar distributions and are not displayed here. (<b>B1</b>)–(<b>B3</b>) are estimated for the autosomal locus in the fat tissue. Estimates for the same locus in the blood tissue show similar distributions and are not displayed here. (<b>C</b>) is estimated from the data in Goyal et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#pone.0032225-Goyal1" target="_blank">[11]</a>, one of the four in vitro data sets on mouse DNMT1 we analyze here. Dark lines indicate the density of a uniform (0,1) prior distribution. Except for the plots in red, which have most probability mass around small values, all the other plots are displayed on the same support of (0,1).</p

Emission probabilities of the HMM.

<p>Subscript denotes the -th methylation pattern, and the -th CpG site. Note that denotes the association (1) or non-association (0) state of DNMT1, parent-strand DNMT3s, and daughter-strand DNMT3s, respectively. Also, denotes the methylated (1) or unmethylated (0) state of CpG on the parent strand and daughter strand, respectively. Additionally, denotes the probability of the -th CpG site being methylated before DNA replication, which is equivalent to the methylation density of the -th site. and are the probability of the maintenance activity of DNMT1 and the DNMT3s, respectively, at associated daughter-strand CpG, whereas and are that of the de novo activity of DNMT1 and the DNMT3s, respectively. The measurement error rates (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#s4" target="_blank">Materials and Methods</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0032225#pone-0032225-t004" target="_blank">Table 4</a>) are assumed to be 0 here. This HMM allows for estimation of the hemi-preference ratio for both DNMT1 and the DNMT3s, although additional constraints are needed for this simultaneous estimation. See text for details.</p

Effect of dietary cadmium on genome-wide 5mC levels in DNA of the hepatopancreas of <i>C</i>. <i>aspersus</i> adults.

<p>(<b>A</b>) The mean contents of 5mC in hepatopancreas DNA in each treatment group at each time point. (<b>B</b>) Estimated marginal means for dietary dose (as the main effect). (<b>C</b>) Estimated marginal means for time (as the main effect). Four snails were sampled for each treatment group at each time point (14, 28, and 56 days). Data are shown on a log₁₀ scale as mean (point) with one standard error (box) and one standard deviation (error bar). In Fig 2A the outliers (white circles) and the extremes (whiskers) are also given (if they exist). Marked boxes(*) indicate significant differences as compared to the reference group (Newman-Keuls test, ***—<i>p</i> < 0.001, **—<i>p</i> < 0.01, *—<i>p</i> < 0.05).</p

Survival times and mortalities for each time period.

<p>Survival times and mortalities for each time period.</p