BACKGROUND
the fact that amplification methods vary in efficiency across the genome has often been noted, for example in whole genome amplification , next generation sequencing, genome wide snp genotyping, and pcr  <cit> .
difficult to assay regions are somewhat correlated with high c + g content  <cit> , but this relationship is complex, dna sample dependent, and incompletely understood.
regions of high c + g content tend to resist the essential dna denaturation step at the initiation of nearly all dna amplification protocols, though it is assumed that this effect will not be so extreme as to completely prevent dna strand separation.
however, this assumption may be incorrect.
in dna melting studies in the early 1970s, select human genome dna fragments were seen to remain double stranded under extreme denaturing conditions  <cit> .
the nature of these challenging sequences has not yet been determined, and today most investigators are probably unaware of the early reports.
here, we investigate a number of genomic regions that across several samples produce low intensity hybridization in illumina infinium genotyping.
we find that a major factor that can influence such regions are intervals of high c + g content that do not denature efficiently under routinely used conditions.
these intervals cause connected dna sequences to rapidly re-anneal and prevent access to primers or probes.
the effects of this in pcr could be completely ameliorated by enzymatic separation of the high c + g interval and the assay target.
we postulate that inter-sample variability is due to the amount and random distribution of nicking within a dna sample which acts to separate these difficult to denature sequences from other dna, and that highly intact dnas will suffer the most.
we provide optimized pcr protocols and suggest that dna is pretreated by either sonication or restriction enzyme digestion prior to amplification steps in methods.
RESULTS
testing dna melting using southern blot hybridisation
to explore the interplay between dna melting and difficult to assay genome regions, we examined large scale illumina infinium snp array datasets  and identified genomic regions within which snps consistently gave weak intensity signals in the poorest performing samples .
we herein refer to these as ‘weak illumina signal’ regions.
single copy dna probes were constructed for ‘weak illumina signal’ and control ‘normal illumina signal’ regions on the long arm of chr  <dig> , to be hybridized on to southern blots.
these blots employed freshly prepared high quality genomic dnas, and each sample was divided into four aliquots so that we could differentially process them by temperature or alkaline denaturation before or after restriction enzyme digestion.
one would expect the denatured dna to migrate differently to dsdna and not give bands of expected restriction fragment sizes upon hybridization with the single copy probes, but any sequences that had fully resisted the denaturation treatments would give such bands.
example results are shown in figure  <dig>  three of three ‘normal illumina signal’ region probes produced the expected ‘no band’ outcome, whereas two of the three ‘weak illumina signal’ region probes generated bands from the denatured samples indicating that these latter regions are generally difficult to denature.
reduced pcr amplification efficiency assessed by prt
we examined normal and ‘weak illumina signal’ regions using the paralogue ratio test   <cit> .
standard prt, which is a powerful technique to genotype copy number variation, employs a single pair of pcr primers to co-amplify a ‘test’ locus  and a ‘reference’ locus  in a single pcr reaction.
the two amplicons are distinguished by size, and their relative product amounts used to determine the test locus copy number.
we adapted this concept to co-amplify single copy sequences from normal and ‘weak illumina signal’ regions.
this allowed the comparison of their relative amplification efficiencies in the same pcr reaction with identical conditions and dna template concentration.
importantly, the ‘test’ and ‘reference’ amplicons employed for six assay designs created for these experiments had similar and not unusually high c + g content .
in all six assays, the ‘reference’ amplicon  produced a strong band, whereas its partnered ‘test’ amplicon produced a weaker band , indicating a reduced pcr efficiency for ‘weak illumina signal’ regions.
enhancing denaturing conditions improves amplification
the above data are consistent with the hypothesis that ‘weak illumina signal’ regions are refractory to amplification and analysis because they are difficult to denature.
to promote dna denaturation in the prt assays, and thereby increase the amplification efficiency of the ‘weak illumina signal’ loci, we tried the following standard denaturing enhancers; including dimethyl sulphoxide  at up to 50%  <cit> ; adding single stranded binding protein  <cit> ; increasing the pcr denaturing temperature to 98°c.
these strategies all helped to improve amplification efficiency, but none of these remedies enabled a full strength intensity gel band to be produced for any of the ‘weak illumina signal’ loci.
adding betaine  <cit>  was more effective, but only at very high concentrations , with the downside of causing overall amplification efficiencies to drop considerably.
most effective was denaturing the input dnas, and snap cooling on ice, prior to inclusion in the pcrs.
however, to significantly improve the amplification efficiencies , it was necessary to heat the samples to 130°c in water for  <dig> minute .
regions of high c + g serve as nuclei for rapid re-annealing of neighboring dna sequences
cumulatively, these findings show that ‘weak illumina signal’ regions are particularly resistant to dna denaturation under standard conditions.
this is true, even when tested pcr amplicons themselves are not particularly c + g rich or unusual in any apparent way .
the implication of this is that locally something other than c + g content of the target sequence is hindering dna strand separation.
direct visualization of genome features represented as tracks on the ucsc genome browser suggests this may have something to do with the very highest peaks of c + g rich sequence coincident with particularly dense clustering of cpg islands .
a possible mechanism could then entail localized regions of extreme c + g content remaining duplexed during standard dna denaturation procedures, and in so doing they would prevent their flanking sequences - that are melted - from diffusing away from each other.
as such, these neighboring strands will be able to quickly re-anneal, following zero-order kinetics, as soon as non-denaturing conditions are re-established  <cit> .
we refer to domains affected by this proposed phenomenon as "thermodynamically ultra fastened"  regions.
to test the tuf hypothesis, we started by looking for localized, highly c + g rich dna elements in the immediate vicinity of the ‘weak illumina signal’ region amplicons for the six prt assays.
such elements were clearly present in five cases.
we then targeted one particular assay  and digested the template dna with various restriction enzymes before running the prt.
dna amplification was seen to be problematic only when the ‘test’ amplicon was located in the same dna fragment as the high c + g element .
in fact, the amplification efficiency was fully restored when the ‘test’ amplicon was separated from the high c + g element, a finding consistent with the tuf hypothesis.
genome wide patterns of tuf
to explore the tuf phenomenon genome wide, we utilized data from  <dig> illumina genotyping runs  <cit>  and, on a sample by sample basis, regressed the log probe intensity ratio  on eight c + g and eight cpg terms for genomic window sizes of  <dig> bp to  <dig> mbp.
the residual variance prior to and after adjustment for c + g and cpg is shown in figure  <dig>  the samples that showed the largest correlations with the c + g and cpg terms, measured by the proportion of lrr variance explained, involved c + g content size windows of  <dig>  -  <dig> kb , and were also observed with a lower significance with cpg content and other window sizes.
we then experimentally tested the amplification behavior of dnas for samples for which the correlation was extreme , plus  <dig> other dnas where no significant correlation was apparent, using two prt assays .
a strong statistical association was seen between prt performance and the per sample extreme behavior on the illumina platform when considering the smaller size windows , as shown in table  <dig>  this fits perfectly with the notion that many particularly c + g rich elements  across the genome influence the efficiency of analysis of surrounding contiguous sequences by severely hindering dna denaturation.
these observations imply that it should be possible to bioinformatically predict and partially correct for the effects of tuf areas of the genome and for other phenomena that have been observed to induce similar c + g correlated effects.
diskin et al.
<cit>  demonstrate that c + g-correlated intensity fluctuations  are present in both illumina and affymetrix whole-genome snp microarrays and that c + g content in  <dig> mb windows are highly correlated with intensity  with the amplitude determined by the degree that dna quantity/concentration deviated from the vendor’s recommended level.
efficiency of pcr amplification of short dna fragments  has also been shown to be affected by local c + g-content and some suggestions have been made on how to predict and compensate for such effects  <cit> .
artificial generation or repair of dna nicking/fragmentation
the discovery and descriptive elucidation of tuf allows us to draw several important practical conclusions.
critically, the experimental impact of the phenomenon on any particular dna sample will depend upon how nicked or fragmented that sample is, because the density of strand discontinuities will affect the probability of any particular dna sequence being separated from c + g rich elements.
counter-intuitively, this implies that newly prepared, highly intact dnas will be most vulnerable to tuf induced problems, whereas older and/or more degraded samples will be less affected.
in support of this, we artificially ‘rejuvenated’ nicked, old dnas by ligase treatment , and found that this made them far more susceptible to tuf as measured by our prt assays .
conversely, by artificially introducing nicks and breaks into dna one can overcome the effect of tuf , ensuring highly uniform assay behaviour across genome regions and samples.
this benefit of dna fragmentation was also demonstrated for wga , and for the overall process of illumina infinium genotyping .
in both cases, sonication of the sample prior to each protocol greatly improved the quality and uniformity of the results.
CONCLUSIONS
in summary, our description of tuf represents the important recognition of a phenomenon relevant to many regions of the genome, thus impacting in a sample dependant manner the conduct of genome-wide studies of distinct types of genetic variation in relation to human diseases/traits.
for example, it may well be practically relevant in copy number variation  research and the use of next generation sequencing, where assay behavior can be unpredictable  <cit> .
further work will be required to fully understand the biochemical basis of the tuf regions in order to optimally develop protocols and approaches for large scale genomic analyses.
knowledge of the tuf phenomenon and ways to overcome its deleterious consequences should provide investigators with a more nuanced approach towards handling issues related to c + g content and its effect upon assay robustness and efficiency.

 the fact that amplification methods vary in efficiency across the genome has often been noted, for example in whole genome amplification, next generation sequencing, genome wide snp genotyping, and pcr. difficult to assay regions are somewhat correlated with high c + g content, but this relationship is complex, dna sample dependent, and incompletely understood. regions of high c + g content tend to resist the essential dna denaturation step at the initiation of nearly all dna amplification protocols, though it is assumed that this effect will not be so extreme as to completely prevent dna strand separation. however, this assumption may be incorrect. in dna melting studies in the early 1970s, select human genome dna fragments were seen to remain double stranded under extreme denaturing conditions. the nature of these challenging sequences has not yet been determined, and today most investigators are probably unaware of the early reports. here, we investigate a number of genomic regions that across several samples produce low intensity hybridization in illumina infinium genotyping. we find that a major factor that can influence such regions are intervals of high c + g content that do not denature efficiently under routinely used conditions. these intervals cause connected dna sequences to rapidly re-anneal and prevent access to primers or probes. the effects of this in pcr could be completely ameliorated by enzymatic separation of the high c + g interval and the assay target. we postulate that inter-sample variability is due to the amount and random distribution of nicking within a dna sample which acts to separate these difficult to denature sequences from other dna, and that highly intact dnas will suffer the most. we provide optimized pcr protocols and suggest that dna is pretreated by either sonication or restriction enzyme digestion prior to amplification steps in methods.  testing dna melting using southern blot hybridisation to explore the interplay between dna melting and difficult to assay genome regions, we examined large scale illumina infinium snp array datasets and identified genomic regions within which snps consistently gave weak intensity signals in the poorest performing samples. we herein refer to these as ‘weak illumina signal’ regions. single copy dna probes were constructed for ‘weak illumina signal’ and control ‘normal illumina signal’ regions on the long arm of chr, to be hybridized on to southern blots. these blots employed freshly prepared high quality genomic dnas, and each sample was divided into four aliquots so that we could differentially process them by temperature or alkaline denaturation before or after restriction enzyme digestion. one would expect the denatured dna to migrate differently to dsdna and not give bands of expected restriction fragment sizes upon hybridization with the single copy probes, but any sequences that had fully resisted the denaturation treatments would give such bands. example results are shown in figure three of three ‘normal illumina signal’ region probes produced the expected ‘no band’ outcome, whereas two of the three ‘weak illumina signal’ region probes generated bands from the denatured samples indicating that these latter regions are generally difficult to denature. reduced pcr amplification efficiency assessed by prt we examined normal and ‘weak illumina signal’ regions using the paralogue ratio test. standard prt, which is a powerful technique to genotype copy number variation, employs a single pair of pcr primers to co-amplify a ‘test’ locus and a ‘reference’ locus in a single pcr reaction. the two amplicons are distinguished by size, and their relative product amounts used to determine the test locus copy number. we adapted this concept to co-amplify single copy sequences from normal and ‘weak illumina signal’ regions. this allowed the comparison of their relative amplification efficiencies in the same pcr reaction with identical conditions and dna template concentration. importantly, the ‘test’ and ‘reference’ amplicons employed for six assay designs created for these experiments had similar and not unusually high c + g content. in all six assays, the ‘reference’ amplicon produced a strong band, whereas its partnered ‘test’ amplicon produced a weaker band, indicating a reduced pcr efficiency for ‘weak illumina signal’ regions. enhancing denaturing conditions improves amplification the above data are consistent with the hypothesis that ‘weak illumina signal’ regions are refractory to amplification and analysis because they are difficult to denature. to promote dna denaturation in the prt assays, and thereby increase the amplification efficiency of the ‘weak illumina signal’ loci, we tried the following standard denaturing enhancers; including dimethyl sulphoxide at up to 50%; adding single stranded binding protein; increasing the pcr denaturing temperature to 98°c. these strategies all helped to improve amplification efficiency, but none of these remedies enabled a full strength intensity gel band to be produced for any of the ‘weak illumina signal’ loci. adding betaine was more effective, but only at very high concentrations, with the downside of causing overall amplification efficiencies to drop considerably. most effective was denaturing the input dnas, and snap cooling on ice, prior to inclusion in the pcrs. however, to significantly improve the amplification efficiencies, it was necessary to heat the samples to 130°c in water for minute. regions of high c + g serve as nuclei for rapid re-annealing of neighboring dna sequences cumulatively, these findings show that ‘weak illumina signal’ regions are particularly resistant to dna denaturation under standard conditions. this is true, even when tested pcr amplicons themselves are not particularly c + g rich or unusual in any apparent way. the implication of this is that locally something other than c + g content of the target sequence is hindering dna strand separation. direct visualization of genome features represented as tracks on the ucsc genome browser suggests this may have something to do with the very highest peaks of c + g rich sequence coincident with particularly dense clustering of cpg islands. a possible mechanism could then entail localized regions of extreme c + g content remaining duplexed during standard dna denaturation procedures, and in so doing they would prevent their flanking sequences - that are melted - from diffusing away from each other. as such, these neighboring strands will be able to quickly re-anneal, following zero-order kinetics, as soon as non-denaturing conditions are re-established. we refer to domains affected by this proposed phenomenon as "thermodynamically ultra fastened" regions. to test the tuf hypothesis, we started by looking for localized, highly c + g rich dna elements in the immediate vicinity of the ‘weak illumina signal’ region amplicons for the six prt assays. such elements were clearly present in five cases. we then targeted one particular assay and digested the template dna with various restriction enzymes before running the prt. dna amplification was seen to be problematic only when the ‘test’ amplicon was located in the same dna fragment as the high c + g element. in fact, the amplification efficiency was fully restored when the ‘test’ amplicon was separated from the high c + g element, a finding consistent with the tuf hypothesis. genome wide patterns of tuf to explore the tuf phenomenon genome wide, we utilized data from illumina genotyping runs and, on a sample by sample basis, regressed the log probe intensity ratio on eight c + g and eight cpg terms for genomic window sizes of bp to mbp. the residual variance prior to and after adjustment for c + g and cpg is shown in figure the samples that showed the largest correlations with the c + g and cpg terms, measured by the proportion of lrr variance explained, involved c + g content size windows of - kb, and were also observed with a lower significance with cpg content and other window sizes. we then experimentally tested the amplification behavior of dnas for samples for which the correlation was extreme, plus other dnas where no significant correlation was apparent, using two prt assays. a strong statistical association was seen between prt performance and the per sample extreme behavior on the illumina platform when considering the smaller size windows, as shown in table this fits perfectly with the notion that many particularly c + g rich elements across the genome influence the efficiency of analysis of surrounding contiguous sequences by severely hindering dna denaturation. these observations imply that it should be possible to bioinformatically predict and partially correct for the effects of tuf areas of the genome and for other phenomena that have been observed to induce similar c + g correlated effects. diskin et al. demonstrate that c + g-correlated intensity fluctuations are present in both illumina and affymetrix whole-genome snp microarrays and that c + g content in mb windows are highly correlated with intensity with the amplitude determined by the degree that dna quantity/concentration deviated from the vendor’s recommended level. efficiency of pcr amplification of short dna fragments has also been shown to be affected by local c + g-content and some suggestions have been made on how to predict and compensate for such effects. artificial generation or repair of dna nicking/fragmentation the discovery and descriptive elucidation of tuf allows us to draw several important practical conclusions. critically, the experimental impact of the phenomenon on any particular dna sample will depend upon how nicked or fragmented that sample is, because the density of strand discontinuities will affect the probability of any particular dna sequence being separated from c + g rich elements. counter-intuitively, this implies that newly prepared, highly intact dnas will be most vulnerable to tuf induced problems, whereas older and/or more degraded samples will be less affected. in support of this, we artificially ‘rejuvenated’ nicked, old dnas by ligase treatment, and found that this made them far more susceptible to tuf as measured by our prt assays. conversely, by artificially introducing nicks and breaks into dna one can overcome the effect of tuf, ensuring highly uniform assay behaviour across genome regions and samples. this benefit of dna fragmentation was also demonstrated for wga, and for the overall process of illumina infinium genotyping. in both cases, sonication of the sample prior to each protocol greatly improved the quality and uniformity of the results.  in summary, our description of tuf represents the important recognition of a phenomenon relevant to many regions of the genome, thus impacting in a sample dependant manner the conduct of genome-wide studies of distinct types of genetic variation in relation to human diseases/traits. for example, it may well be practically relevant in copy number variation research and the use of next generation sequencing, where assay behavior can be unpredictable. further work will be required to fully understand the biochemical basis of the tuf regions in order to optimally develop protocols and approaches for large scale genomic analyses. knowledge of the tuf phenomenon and ways to overcome its deleterious consequences should provide investigators with a more nuanced approach towards handling issues related to c + g content and its effect upon assay robustness and efficiency. 
in turn, this behavior creates broader ‘thermodynamically ultra-fastened’ regions characterized by incomplete denaturation of the two dna strands, so reducing amplification efficiency throughout these domains. this model provides a mechanistic explanation for why some genome regions are particularly difficult to amplify and assay in many procedures, and importantly it also explains inter-sample variability of this behavior. a major practical consequence of this is that inter-region and inter-sample variability can be largely overcome by employing routine fragmentation methods prior to sample amplification. the most affected genome regions tend to correlate with high c + g content, however this relationship is complex and does not explain why the direction and magnitude of effects varies considerably between samples.
 for many analytical methods the efficiency of dna amplification varies across the genome and between samples. the most affected genome regions tend to correlate with high c + g content, however this relationship is complex and does not explain why the direction and magnitude of effects varies considerably between samples.  here, we provide evidence that sequence elements that are particularly high in c + g content can remain annealed even when aggressive melting conditions are applied. in turn, this behavior creates broader ‘thermodynamically ultra-fastened’ regions characterized by incomplete denaturation of the two dna strands, so reducing amplification efficiency throughout these domains.  this model provides a mechanistic explanation for why some genome regions are particularly difficult to amplify and assay in many procedures, and importantly it also explains inter-sample variability of this behavior. that is, dna samples of varying quality will carry more or fewer nicks and breaks, and hence their intact tuf regions will have different lengths and so be differentially affected by this amplification suppression mechanism – with ‘higher’ quality dnas being the most vulnerable. a major practical consequence of this is that inter-region and inter-sample variability can be largely overcome by employing routine fragmentation methods prior to sample amplification. dna amplificationdna denaturationc + gillumina infinium 