Early Onset Prion Disease from Octarepeat Expansion Correlates with Copper Binding Properties

Insertional mutations leading to expansion of the octarepeat domain of the prion protein (PrP) are directly linked to prion disease. While normal PrP has four PHGGGWGQ octapeptide segments in its flexible N-terminal domain, expanded forms may have up to nine additional octapeptide inserts. The type of prion disease segregates with the degree of expansion. With up to four extra octarepeats, the average onset age is above 60 years, whereas five to nine extra octarepeats results in an average onset age between 30 and 40 years, a difference of almost three decades. In wild-type PrP, the octarepeat domain takes up copper (Cu2+) and is considered essential for in vivo function. Work from our lab demonstrates that the copper coordination mode depends on the precise ratio of Cu2+ to protein. At low Cu2+ levels, coordination involves histidine side chains from adjacent octarepeats, whereas at high levels each repeat takes up a single copper ion through interactions with the histidine side chain and neighboring backbone amides. Here we use both octarepeat constructs and recombinant PrP to examine how copper coordination modes are influenced by octarepeat expansion. We find that there is little change in affinity or coordination mode populations for octarepeat domains with up to seven segments (three inserts). However, domains with eight or nine total repeats (four or five inserts) become energetically arrested in the multi-histidine coordination mode, as dictated by higher copper uptake capacity and also by increased binding affinity. We next pooled all published cases of human prion disease resulting from octarepeat expansion and find remarkable agreement between the sudden length-dependent change in copper coordination and onset age. Together, these findings suggest that either loss of PrP copper-dependent function or loss of copper-mediated protection against PrP polymerization makes a significant contribution to early onset prion disease.


Supplemental analyses relating age at onset of disease to number of octarepeats (OR)
In addition to the analysis of variance and regression results presented in the main paper, we performed two additional analyses examining how age at disease onset is related to the number of octarepeats (OR). In the first of these analyses, we used a frequentist nonlinear regression method to characterize the mean age as a function of OR number; the second analysis fitted a Bayesian change-point model to the same relationship.
Table 1 (Supplement) gives a descriptive summary of onset age at each observed level of OR number, and Figure 1 (Supplement) presents a scatterplot of age versus OR number, with a cubic regression fit (corresponding to one of the analyses in the main paper), a nonparametric smooth -based on the lowess function (Cleveland, 1979) in the statistical analysis environment R (R Development Core Team, 2003) -and a constant model (at the mean age of 40.2 years) superimposed. This graph is highly suggestive of a strong nonconstant relationship between the two variables, in which -as the number of octarepeats increases -the mean onset age at first declines and then rises again. This can be confirmed by bootstrapping (e.g., Efron and Tibshirani, 1993) the lowess function, as in Figure 2 (Supplement); the vertical envelope of dotted lines in the figure for any OR number provides an approximate 99% nonparametric interval estimate for the median age at onset for that OR number. It is clear that the underlying relationship in the population of individuals similar to those in our study is non-constant.
The problem of testing for a difference in the onset age among individuals with different numbers of octarepeats can also be tackled using a model that assumes that the onset age is a piecewise-constant function of the OR number, possibly with one single change-point after an undetermined number of repeats. As an alternative analysis we also fit this model, commonly known as a single change-point model, using Bayesian methods (e.g., Robert, 2007), which require the elicitation of prior distributions that, combined with the information in the data, produce posterior probability distributions upon which inference is based.  In brief, our model assumed that the patients are divided in up to two groups (above and below an unknown number of repeats) and that the onset ages within each group follow a Normal distribution with unknown parameters. With 9 observed OR number values in our data set, testing for differences and identifying the unknown change-point effectively reduced to comparing 9 models: the model that assumes no change point in the data (to which we assigned a prior probability of 1 2 , and the 8 models corresponding to a change-point after each OR number (each of which was given a prior probability of 1 16 , which means that, a priori, we think that a change point has the same probability of occurring after any number of repeats). For the other unknown parameters in the model (the mean and variance of each group) we employ conjugate Normal-Inverse-Gamma priors, with parameters chosen to reflect historical information from previous studies. The priors we used in this analysis implied that the average onset age has a mean of 50 years, and that we expect it to be between 0 and 100 years with roughly 95% probability. We further assumed that the standard deviation of the onset age within each group is around 12 years and has a 95% probability of being below 25 years.
With these conjugate priors, closed-form expressions for the posterior probabilities of the 9 models involved can readily be obtained, allowing us to avoid Monte Carlo integration (the calculations are straightforward and are therefore omitted). The posterior probability (given the data) for the model with no change point was 1.3·10 −12 , which provides decisive evidence against a model in which onset age does not depend on OR number. (The fact that this probability is so small also makes it clear that even dramatic changes, for sensitivity analysis purposes, in the prior probabilities for the no-change-point and one-change-point models would have no effect on this conclusion.) In terms of the location of the change-point, there was decisive evidence of a change in the average onset age after either 4 or 5 repeats, but the exact location of the change-point was not completely clear: the posterior probability for a change between 4 and 5 repeats was 0.72, while the probability of a change between 5 and 6 repeats was 0.27 (all other locations for the change point had posterior probabilities of less than 10 −6 ). Sensitivity analysis showed that, overall, these results were fairly robust to moderate changes in the prior distribution; for example, a prior mean for the average onset age of around 40 years roughly evened out the posterior probabilities of the change-points at 4/5 or 5/6. These results are broadly consistent with those we described in the main text of the paper and with the results presented earlier in this section.

Supplemental analyses relating duration of disease to OR number
We also performed additional analyses examining the relationship between disease duration and octarepeat number. Table 2 (Supplement) presents a descriptive summary of disease duration at each observed level of OR number; disease duration was heavily positively skewed, suggesting a logarithmic transformation. The top panel in Figure 3 (Supplement) gives a scatterplot of the logarithm of disease duration as a function of number of repeats, with a cubic regression fit (corresponding to one of the analyses in the main paper) and a nonparametric smooth (red solid curve) superimposed, and with a constant model at the mean log duration (1.3) for comparison. Once again it is evident that the relationship is strongly nonconstant; once again, to confirm this the lowess nonparametric smooth can be bootstrapped, as in the bottom panel in Figure 3 (Supplement). Here there is more vertical uncertainty than in Figure 2 (Supplement), but significant departures from a constant model are again evident.
As noted in the main text, we used an ANOVA of log(duration) on OR number, followed by multiple-comparison-adjusted pairwise comparisons of means, to find statistically significant  differences in the relationship between disease duration and number of octarepeats. We conclude with a summary, in Table 3 (Supplement), of the pairwise differences found significant at the 0.05 level by the Tukey-Kramer HSD method.