Background RNA editing is the process whereby an RNA sequence is modified from the sequence of the corresponding DNA template. In the mitochondria of land plants, some cytidines are converted to uridines before translation. Despite substantial study, the molecular biological mechanism by which C-to-U RNA editing proceeds remains relatively obscure, although several experimental studies have implicated a role for  cis -recognition. A highly non-random distribution of nucleotides is observed in the immediate vicinity of edited sites (within 20 nucleotides 5' and 3'), but no precise consensus motif has been identified.
Background
RNA editing is the process whereby an RNA sequence is modified from the sequence of the corresponding DNA template. In the mitochondria of land plants, some cytidines are converted to uridines before translation. Despite substantial study, the molecular biological mechanism by which C-to-U RNA editing proceeds remains relatively obscure, although several experimental studies have implicated a role for  cis -recognition. A highly non-random distribution of nucleotides is observed in the immediate vicinity of edited sites (within 20 nucleotides 5' and 3'), but no precise consensus motif has been identified.cisResults Data for analysis were derived from the the complete mitochondrial genomes of  Arabidopsis thaliana ,  Brassica napus , and  Oryza sativa ; additionally, a combined data set of observations across all three genomes was generated. We selected datasets based on the 20 nucleotides 5' and the 20 nucleotides 3' of edited sites and an equivalently sized and appropriately constructed null-set of non-edited sites. We used tree-based statistical methods and random forests to generate models of C-to-U RNA editing based on the nucleotides surrounding the edited/non-edited sites and on the estimated folding energies of those regions. Tree-based statistical methods based on primary sequence data surrounding edited/non-edited sites and estimates of free energy of folding yield models with optimistic re-substitution-based estimates of ~0.71 accuracy, ~0.64 sensitivity, and ~0.88 specificity. Random forest analysis yielded better models and more exact performance estimates with ~0.74 accuracy, ~0.72 sensitivity, and ~0.81 specificity for the combined observations.
Results
Data for analysis were derived from the the complete mitochondrial genomes of  Arabidopsis thaliana ,  Brassica napus , and  Oryza sativa ; additionally, a combined data set of observations across all three genomes was generated. We selected datasets based on the 20 nucleotides 5' and the 20 nucleotides 3' of edited sites and an equivalently sized and appropriately constructed null-set of non-edited sites. We used tree-based statistical methods and random forests to generate models of C-to-U RNA editing based on the nucleotides surrounding the edited/non-edited sites and on the estimated folding energies of those regions. Tree-based statistical methods based on primary sequence data surrounding edited/non-edited sites and estimates of free energy of folding yield models with optimistic re-substitution-based estimates of ~0.71 accuracy, ~0.64 sensitivity, and ~0.88 specificity. Random forest analysis yielded better models and more exact performance estimates with ~0.74 accuracy, ~0.72 sensitivity, and ~0.81 specificity for the combined observations.Arabidopsis thalianaBrassica napusOryza sativaConclusions Simple models do moderately well in predicting which cytidines will be edited to uridines, and provide the first quantitative predictive models for RNA edited sites in plant mitochondria. Our analysis shows that the identity of the nucleotide -1 to the edited C and the estimated free energy of folding for a 41 nt region surrounding the edited C are the most important variables that distinguish most edited from non-edited sites. However, the results suggest that primary sequence data and simple free energy of folding calculations alone are insufficient to make highly accurate predictions.
Conclusions
Simple models do moderately well in predicting which cytidines will be edited to uridines, and provide the first quantitative predictive models for RNA edited sites in plant mitochondria. Our analysis shows that the identity of the nucleotide -1 to the edited C and the estimated free energy of folding for a 41 nt region surrounding the edited C are the most important variables that distinguish most edited from non-edited sites. However, the results suggest that primary sequence data and simple free energy of folding calculations alone are insufficient to make highly accurate predictions.

Background RNA editing is the process whereby an RNA sequence is modified from the sequence corresponding to the DNA template. A particular form of RNA editing in plant mitochondria, by which some cytidines are converted to uridines before translation, occurs in many land plant lineages. Although cytidine to uridine conversion is most common, the reverse conversion is sometimes observed [ 1 - 4 ]. In plants, the phenomenon is best studied, albeit still poorly understood, in the mitochondria and plastids of angiosperms [ 5 - 8 ]. The majority of plant mitochondrial RNA editing occurs in coding sequences, and editing frequently changes codons, resulting in changes of amino acids, or, in some cases, creation of entirely new open reading frames [ 1 , 9 , 10 ]. These changes often result in an increase in similarity with respect to homologous protein sequences among different organisms (such as in wheat [ 11 ]), and Gray has postulated that the RNA editing process functions as a repair mechanism to correct otherwise-deleterious genomic mutations [ 12 ]. RNA editing has also been detected in introns, where it is conjectured to improve splicing efficiency [ 13 ]. The precise biochemical basis for C-to-U editing in plant mitochondria is unknown, although experimental evidence suggests a deamination reaction [ 14 - 18 ]. Despite substantial study, the molecular biological mechanism by which C-to-U RNA editing proceeds remains relatively obscure, although several experimental studies have implicated a role for  cis -recognition [ 19 - 21 ]. The mechanism by which edited sites are recognized is also still poorly understood, but the importance of surrounding nucleotides has been noted [ 22 ]. A highly non-random distribution of nucleotides in the immediate vicinity of edited sites (within 10–20 nucleotides 5' and 3') is observed, but no precise consensus motif has been identified [ 9 , 16 ]. Additionally, previous studies suggest that inferred secondary structure is not important in site recognition for C-to-U conversion [ 16 , 19 ]. Identifying edited sites thus remains an open problem, one to which we have applied tree-based statistical models and an extension of such models. When applied to a similar problem (predicting peptide binding to major histocompatibility complex (MHC) class I molecules [ 23 ]), tree-based statistical methods generated very accurate models, identifying specific important residues when no precise sequence motif had previously been identified. Therefore, we were motivated to apply tree-based statistical models and an extension, random forests, to the problem of C-to-U RNA editing in angiosperm mitochondria using complete mitochondrial genome data for three species:  Arabidopsis thaliana ,  Brassica napus  and  Oryza sativa . The objective for the current research was to identify sequence features that may provide insights into C-to-U editing of plant mitochondrial RNA. We address the following specific questions. Is there evidence that sufficient information exists within sequence regions flanking edited sites to accurately predict editing? Is there an association between estimated free energy of folding for short sequence regions containing edited sites and C-to-U editing? We report tree-based statistical analysis of three complete mitochondrial genomes and show that relatively simple models provide moderately accurate prediction of C-to-U edited sites.
Background
RNA editing is the process whereby an RNA sequence is modified from the sequence corresponding to the DNA template. A particular form of RNA editing in plant mitochondria, by which some cytidines are converted to uridines before translation, occurs in many land plant lineages. Although cytidine to uridine conversion is most common, the reverse conversion is sometimes observed [ 1 - 4 ]. In plants, the phenomenon is best studied, albeit still poorly understood, in the mitochondria and plastids of angiosperms [ 5 - 8 ].The majority of plant mitochondrial RNA editing occurs in coding sequences, and editing frequently changes codons, resulting in changes of amino acids, or, in some cases, creation of entirely new open reading frames [ 1 , 9 , 10 ]. These changes often result in an increase in similarity with respect to homologous protein sequences among different organisms (such as in wheat [ 11 ]), and Gray has postulated that the RNA editing process functions as a repair mechanism to correct otherwise-deleterious genomic mutations [ 12 ]. RNA editing has also been detected in introns, where it is conjectured to improve splicing efficiency [ 13 ].The precise biochemical basis for C-to-U editing in plant mitochondria is unknown, although experimental evidence suggests a deamination reaction [ 14 - 18 ]. Despite substantial study, the molecular biological mechanism by which C-to-U RNA editing proceeds remains relatively obscure, although several experimental studies have implicated a role for  cis -recognition [ 19 - 21 ]. The mechanism by which edited sites are recognized is also still poorly understood, but the importance of surrounding nucleotides has been noted [ 22 ]. A highly non-random distribution of nucleotides in the immediate vicinity of edited sites (within 10–20 nucleotides 5' and 3') is observed, but no precise consensus motif has been identified [ 9 , 16 ]. Additionally, previous studies suggest that inferred secondary structure is not important in site recognition for C-to-U conversion [ 16 , 19 ].cisIdentifying edited sites thus remains an open problem, one to which we have applied tree-based statistical models and an extension of such models. When applied to a similar problem (predicting peptide binding to major histocompatibility complex (MHC) class I molecules [ 23 ]), tree-based statistical methods generated very accurate models, identifying specific important residues when no precise sequence motif had previously been identified. Therefore, we were motivated to apply tree-based statistical models and an extension, random forests, to the problem of C-to-U RNA editing in angiosperm mitochondria using complete mitochondrial genome data for three species:  Arabidopsis thaliana ,  Brassica napus  and  Oryza sativa . The objective for the current research was to identify sequence features that may provide insights into C-to-U editing of plant mitochondrial RNA. We address the following specific questions. Is there evidence that sufficient information exists within sequence regions flanking edited sites to accurately predict editing? Is there an association between estimated free energy of folding for short sequence regions containing edited sites and C-to-U editing? We report tree-based statistical analysis of three complete mitochondrial genomes and show that relatively simple models provide moderately accurate prediction of C-to-U edited sites.Arabidopsis thalianaBrassica napusOryza sativaResults Tree-based statistical models Analysis of each of the three species-specific mitochondrial genome data sets yielded substantially similar results (Table  1 ). Using flanking nucleotides and estimates of folding energy as predictor variables, the optimistic re-substitution-based estimates for cross-validated pruned models had a mean correct classification rate of 0.705 (sensitivity [the proportion of observations correctly identified as edited]   = 0.640, and specificity [the proportion of observations correctly identified as non-edited]   = 0.883) across the three species. As an additional classification tree analysis, we examined a dataset generated by combining the data from the three species. These results were generally similar to those described above for the mean of the individual genome datasets. The classification tree model is shown in Figure  1 ; the partition is defined based on the nucleotide immediately 5' (-1 position) of the edited/non-edited site. Of the 1972 observations with pyrimidine at the -1 position, 1262 (0.64) are edited and 710 (0.36) are non-edited sites. Of the 722 observations with purine at the -1 position, 85 (0.12) are edited and 637 (0.88) are non-edited sites. Random forests Results from random forests (Table  2 ) were very similar to those obtained with classification trees and were somewhat more accurate. In single-species analyses, the mean accuracy rate was 0.744 (sensitivity   = 0.717, specificity   = 0.809). Analysis of the larger, combined data set yielded a model better than any of the single genome models with an accuracy of 0.848 (Table  2 ). Analysis of variable importance showed that the -1 position is overwhelmingly the most important factor in determining editing status. Other variables of lesser predictive value include estimated free energy of folding, and the -2 and +1 positions relative to the edited/non-edited site (Figure  2 ).
Results
Tree-based statistical models Analysis of each of the three species-specific mitochondrial genome data sets yielded substantially similar results (Table  1 ). Using flanking nucleotides and estimates of folding energy as predictor variables, the optimistic re-substitution-based estimates for cross-validated pruned models had a mean correct classification rate of 0.705 (sensitivity [the proportion of observations correctly identified as edited]   = 0.640, and specificity [the proportion of observations correctly identified as non-edited]   = 0.883) across the three species. As an additional classification tree analysis, we examined a dataset generated by combining the data from the three species. These results were generally similar to those described above for the mean of the individual genome datasets. The classification tree model is shown in Figure  1 ; the partition is defined based on the nucleotide immediately 5' (-1 position) of the edited/non-edited site. Of the 1972 observations with pyrimidine at the -1 position, 1262 (0.64) are edited and 710 (0.36) are non-edited sites. Of the 722 observations with purine at the -1 position, 85 (0.12) are edited and 637 (0.88) are non-edited sites.
Tree-based statistical models
Analysis of each of the three species-specific mitochondrial genome data sets yielded substantially similar results (Table  1 ). Using flanking nucleotides and estimates of folding energy as predictor variables, the optimistic re-substitution-based estimates for cross-validated pruned models had a mean correct classification rate of 0.705 (sensitivity [the proportion of observations correctly identified as edited]   = 0.640, and specificity [the proportion of observations correctly identified as non-edited]   = 0.883) across the three species.As an additional classification tree analysis, we examined a dataset generated by combining the data from the three species. These results were generally similar to those described above for the mean of the individual genome datasets. The classification tree model is shown in Figure  1 ; the partition is defined based on the nucleotide immediately 5' (-1 position) of the edited/non-edited site. Of the 1972 observations with pyrimidine at the -1 position, 1262 (0.64) are edited and 710 (0.36) are non-edited sites. Of the 722 observations with purine at the -1 position, 85 (0.12) are edited and 637 (0.88) are non-edited sites.Random forests Results from random forests (Table  2 ) were very similar to those obtained with classification trees and were somewhat more accurate. In single-species analyses, the mean accuracy rate was 0.744 (sensitivity   = 0.717, specificity   = 0.809). Analysis of the larger, combined data set yielded a model better than any of the single genome models with an accuracy of 0.848 (Table  2 ). Analysis of variable importance showed that the -1 position is overwhelmingly the most important factor in determining editing status. Other variables of lesser predictive value include estimated free energy of folding, and the -2 and +1 positions relative to the edited/non-edited site (Figure  2 ).
Random forests
Results from random forests (Table  2 ) were very similar to those obtained with classification trees and were somewhat more accurate. In single-species analyses, the mean accuracy rate was 0.744 (sensitivity   = 0.717, specificity   = 0.809). Analysis of the larger, combined data set yielded a model better than any of the single genome models with an accuracy of 0.848 (Table  2 ). Analysis of variable importance showed that the -1 position is overwhelmingly the most important factor in determining editing status. Other variables of lesser predictive value include estimated free energy of folding, and the -2 and +1 positions relative to the edited/non-edited site (Figure  2 ).Discussion Despite their simplicity, the tree-based statistical models derived here performed moderately well, with mean accuracies across species generally ~0.71. Single trees were improved upon by constructing models based on ensembles of tree-based models (random forests) each of which was built using random subsamples of the data. This sub-sampling has the effect of reducing the variance through averaging and also reducing the correlation among models. One of the advantages that random forests have over single classification trees is that they provide quantitative measures of variable importance, whereas with a simple classification tree, one is primarily limited to inferring variable importance from the frequency and location of the occurrence of variables in the model. One measure of variable importance is the decrease in the Gini index (a measure of impurity of observations at a particular node) induced by splitting on the variable, averaged over all trees [ 24 ]. In order to infer the relative importance of the predictor variables, we considered the measure of variable importance produced during the random forest run on the combined dataset, which is the most broadly representative dataset considered here. A plot of the variable importance measure for this dataset is shown in Figure  2 ; more important variables are shown as higher bars. The measure strongly indicates that the residue immediately 5' of the edited site (-1 position) is very important. These variable importance results are in agreement with previous work on C-to-U editing in mitochondria of  Arabidopsis thaliana,  which noted the -1, and -2 positions had highly non-random nucleotide distributions [ 9 ]. However, the results here differ from the past study of  Arabidopsis  in that we find no indication that the -17 position has much importance in edited site recognition. Also previously noted was that for 93.1% of the time [ 9 ], the -1 position contained a pyrimidine, which is the data partition found by the classification trees. The free energy results contrast with previous studies indicating that secondary structure was not important in edited site recognition [ 16 , 19 ]. Our results show free energy is a relatively important variable in the random forest analyses. These results therefore indicate that secondary structure, as measured by free energy of folding for the 41 nt region centered on an edited/non-edited site, does help in distinguishing edited from non-edited sites. Previous studies determined putative secondary structures for mRNA regions containing edited sites and looked for conserved structural motifs. In contrast, we used estimates of free energy of folding, which are much easier to compare quantitatively. It may be that secondary or tertiary structure is even more important in determining edited sites than shown here; however, secondary structure may not be effectively represented by the calculated estimates of free energy of folding analyzed.
Discussion
Despite their simplicity, the tree-based statistical models derived here performed moderately well, with mean accuracies across species generally ~0.71. Single trees were improved upon by constructing models based on ensembles of tree-based models (random forests) each of which was built using random subsamples of the data. This sub-sampling has the effect of reducing the variance through averaging and also reducing the correlation among models.One of the advantages that random forests have over single classification trees is that they provide quantitative measures of variable importance, whereas with a simple classification tree, one is primarily limited to inferring variable importance from the frequency and location of the occurrence of variables in the model. One measure of variable importance is the decrease in the Gini index (a measure of impurity of observations at a particular node) induced by splitting on the variable, averaged over all trees [ 24 ].In order to infer the relative importance of the predictor variables, we considered the measure of variable importance produced during the random forest run on the combined dataset, which is the most broadly representative dataset considered here. A plot of the variable importance measure for this dataset is shown in Figure  2 ; more important variables are shown as higher bars. The measure strongly indicates that the residue immediately 5' of the edited site (-1 position) is very important. These variable importance results are in agreement with previous work on C-to-U editing in mitochondria of  Arabidopsis thaliana,  which noted the -1, and -2 positions had highly non-random nucleotide distributions [ 9 ]. However, the results here differ from the past study of  Arabidopsis  in that we find no indication that the -17 position has much importance in edited site recognition. Also previously noted was that for 93.1% of the time [ 9 ], the -1 position contained a pyrimidine, which is the data partition found by the classification trees.Arabidopsis thaliana,ArabidopsisThe free energy results contrast with previous studies indicating that secondary structure was not important in edited site recognition [ 16 , 19 ]. Our results show free energy is a relatively important variable in the random forest analyses. These results therefore indicate that secondary structure, as measured by free energy of folding for the 41 nt region centered on an edited/non-edited site, does help in distinguishing edited from non-edited sites. Previous studies determined putative secondary structures for mRNA regions containing edited sites and looked for conserved structural motifs. In contrast, we used estimates of free energy of folding, which are much easier to compare quantitatively. It may be that secondary or tertiary structure is even more important in determining edited sites than shown here; however, secondary structure may not be effectively represented by the calculated estimates of free energy of folding analyzed.Conclusions Simple models based on nucleotides surrounding edited/non-edited sites and on estimated folding energies of those regions provide moderately accurate prediction of C-to-U RNA edited sites. More nuanced representation of secondary or higher-order structure in combination with variables based on the nucleotide positions found important here might improve models. Overall, the results strongly suggest that the C-to-U editing mechanism in plant mitochondria does not depend exclusively on the primary sequence immediately in the vicinity of the edited site.
Conclusions
Simple models based on nucleotides surrounding edited/non-edited sites and on estimated folding energies of those regions provide moderately accurate prediction of C-to-U RNA edited sites. More nuanced representation of secondary or higher-order structure in combination with variables based on the nucleotide positions found important here might improve models. Overall, the results strongly suggest that the C-to-U editing mechanism in plant mitochondria does not depend exclusively on the primary sequence immediately in the vicinity of the edited site.Methods Data sources We obtained complete mitochondrial genome sequences and information regarding edited sites from GenBank [ 25 ] for three species:  Arabidopsis thaliana  (L.) Heynh. (mouse-ear cress), 455 edited sites, GenBank accession number NC_001284 [ 9 ];  Brassica napus  L. (rapeseed), 425 edited sites, GenBank accession number AP006444 [ 26 ]; and  Oryza sativa  L (rice), 486 edited sites, GenBank accession numbers AB076665 and AB076666 [ 27 ]. None of the GenBank entries noted U-to-C RNA edited sites. Variable selection Incomplete annotations in the GenBank sequences required us to algorithmically determine on which strand an edited site fell (the GenBank files sometimes supplied only a position number, with no strand information). The algorithm, implemented in a Perl script, scanned the entire GenBank file and built an in-memory representation of the layout of all genes and coding sequence regions in the genome. The strand with which an edited site was associated could then be determined by consulting the resultant genome map and checking which strand at the edited site contained a gene region. In no case were genes on both strands at an edited site, so strand localization was always unambiguous. In a few cases, however, a gene containing an edited site could not be located, or a site marked as a C-to-U edit did not contain a C in either strand. In these cases, the supposed edited site was eliminated from further consideration. Final numbers of included sites were as follows:  Arabidopsis , 444;  Brassica , 422;  Oryza , 481. In total, 19 edited sites in the GenBank files were not included across all three species. We also constructed a set of null observations of cytidines that are not edited to uridines. In constructing a null-set, it is important to ensure that the observations are as alike as possible to the edited observations (differing only in the trait to be measured), or the resulting model may be fictive. Here, our null-set observations were non-edited cytidines chosen at random from within gene regions of the genome. Additionally, we chose cytidines such that the null set had exactly the same distribution of codon positions as did the edited set, because the distribution of edited sites within the three possible positions of a codon is highly non-random with a bias to the first two positions [ 9 ] (Table  3 ). For each observation, we recorded 40 nucleotide state variables: one variable for each of the 20 nucleotides sites 5' and 3' of the edited C (on the same strand). We chose a value of 20 for the number of nucleotides 5' and 3' so as to encompass the entire range of semi-conserved positions previously suggested, the most extreme of which occurs 17 bases 5' of the edited site [ 9 ]. In some cases other edited sites occurred within the 20 nucleotides 5' and 3' of the edited site used as a response variable. In these cases the edited sites as predictor variables were recorded as C. The low frequency of these sites at a particular position with respect to other edited sites results in non-significant effects, independent of how these sites are handled. In those cases where a full 20 nucleotides were not included within an annotated mRNA, the missing nucleotides were treated as unknown. Additionally, we included two variables based on free energy expressed in units of kcal/mole at 20°C: the estimated free energy of folding for each 41-nucleotide sequence (20 bases 5', the edited/non-edited base, 20 bases 3') and the change in free energy of folding between the non-edited and edited versions of the 41-nucleotide sequence. Free energies of folding were calculated using mfold [ 28 , 29 ] version 3.1 with program parameters except temperature at default values. Finally, we included codon position as a variable, even though the null set had been chosen so non-edited sites had the same distribution of codon position as the edited sites, as shown in Table  3 . Including codon position as a predictor variable allows for possible interactions with other variables. Finally, we created a combined data set to use alongside the species-specific datasets. The combined dataset is the result of combining all edited sites from all three species (there were no observations identical in all predictor variables), and then randomly selecting negative examples from the set of those already chosen for the three individual datasets. Negative examples were chosen to exactly match the positive examples in distribution over both species and codon position. The combined dataset comprises 2,694 observations. Data analysis Tree-based statistical models We used the R language for statistical computing [ 30 ], version 1.7.1 to conduct our analyses. Analyses included tree-based statistical models using rpart [ 31 ] and random forests using the FORTRAN implementation of random forest version 3.1 [ 24 , 32 ]. Tree-based statistical models [ 33 ], also known as classification and regression trees (CART) [ 34 ], are generated by recursively creating binary partitions of a dataset. Each partition is based on the value of a single predictor variable chosen to best produce homogeneous collections of a nominal or ordinal response variable (classification) or to best separate low and high values of a continuous response variable (regression). More precisely, the partitions may be considered as questions of the following form: Is the observation x i  ∈  A ? Where  A  is a region of the variable space defined by some criterion of a single predictor variable. Answering such a question for all observations produces two groups: those observations for which the answer is  yes  (those in region  A ) and those for which the answer is  no  (x i  ∉  A , those in  ). Subsequent binary partitioning continues until stopping criteria (variously defined) are met [ 34 ]. The result is a classification or a regression tree: a hierarchical series of data bifurcations that depicts the partition definitions and describes the resulting data subsets defined by each partition. To address concerns about possible over-fitting models to the data we used 10-fold cross-validation and pruned trees to the shortest within 1- SE  of the best tree. We assessed the significance of our tree-based statistical models through permutation where the predictor variables are randomized with respect to the response variable [ 35 ]. The frequency of observing a result value equal to or better than the observed value in 1 × 10 4  permutations is the estimate of the probability associated with the observed result. Random forests If one tree-based statistical model is good, then an ensemble (forest) of appropriately constructed tree models should be even better, which is the principal idea of random forests. A random forest attempts to improve upon a simple tree-based statistical model by generating a collection of such models and using them in aggregate [ 24 , 32 ]. Each model in a random forest is generated from a bootstrap sample of the original dataset, and at each node in each model a search for the best possible split is through a subset of variables selected at random from the bootstrap sample of predictor variables. These randomization steps decrease prediction error through variance reduction resulting from averaging and by decreasing the correlation between individual models in the ensemble [ 36 , 37 ]. Each of our random forest analyses comprised 1 × 10 4  individual models constructed by sub-sampling seven predictor variables at each node. Several model summary statistics were calculated, including sensitivity, which is the proportion of observations correctly identified as edited, specificity, which is the proportion of observations correctly identified as non-edited, and accuracy, which is the total proportion of observations correctly identified. More formally, these definitions are: sensitivity = true positives/ ( true positives  +  false negatives ); specificity = true negatives/ ( true negatives  +  false positives ); and accuracy  = ( true positives  +  true negatives )/ total .
Methods
Data sources We obtained complete mitochondrial genome sequences and information regarding edited sites from GenBank [ 25 ] for three species:  Arabidopsis thaliana  (L.) Heynh. (mouse-ear cress), 455 edited sites, GenBank accession number NC_001284 [ 9 ];  Brassica napus  L. (rapeseed), 425 edited sites, GenBank accession number AP006444 [ 26 ]; and  Oryza sativa  L (rice), 486 edited sites, GenBank accession numbers AB076665 and AB076666 [ 27 ]. None of the GenBank entries noted U-to-C RNA edited sites.
Data sources
We obtained complete mitochondrial genome sequences and information regarding edited sites from GenBank [ 25 ] for three species:  Arabidopsis thaliana  (L.) Heynh. (mouse-ear cress), 455 edited sites, GenBank accession number NC_001284 [ 9 ];  Brassica napus  L. (rapeseed), 425 edited sites, GenBank accession number AP006444 [ 26 ]; and  Oryza sativa  L (rice), 486 edited sites, GenBank accession numbers AB076665 and AB076666 [ 27 ]. None of the GenBank entries noted U-to-C RNA edited sites.Arabidopsis thalianaBrassica napusOryza sativaVariable selection Incomplete annotations in the GenBank sequences required us to algorithmically determine on which strand an edited site fell (the GenBank files sometimes supplied only a position number, with no strand information). The algorithm, implemented in a Perl script, scanned the entire GenBank file and built an in-memory representation of the layout of all genes and coding sequence regions in the genome. The strand with which an edited site was associated could then be determined by consulting the resultant genome map and checking which strand at the edited site contained a gene region. In no case were genes on both strands at an edited site, so strand localization was always unambiguous. In a few cases, however, a gene containing an edited site could not be located, or a site marked as a C-to-U edit did not contain a C in either strand. In these cases, the supposed edited site was eliminated from further consideration. Final numbers of included sites were as follows:  Arabidopsis , 444;  Brassica , 422;  Oryza , 481. In total, 19 edited sites in the GenBank files were not included across all three species. We also constructed a set of null observations of cytidines that are not edited to uridines. In constructing a null-set, it is important to ensure that the observations are as alike as possible to the edited observations (differing only in the trait to be measured), or the resulting model may be fictive. Here, our null-set observations were non-edited cytidines chosen at random from within gene regions of the genome. Additionally, we chose cytidines such that the null set had exactly the same distribution of codon positions as did the edited set, because the distribution of edited sites within the three possible positions of a codon is highly non-random with a bias to the first two positions [ 9 ] (Table  3 ). For each observation, we recorded 40 nucleotide state variables: one variable for each of the 20 nucleotides sites 5' and 3' of the edited C (on the same strand). We chose a value of 20 for the number of nucleotides 5' and 3' so as to encompass the entire range of semi-conserved positions previously suggested, the most extreme of which occurs 17 bases 5' of the edited site [ 9 ]. In some cases other edited sites occurred within the 20 nucleotides 5' and 3' of the edited site used as a response variable. In these cases the edited sites as predictor variables were recorded as C. The low frequency of these sites at a particular position with respect to other edited sites results in non-significant effects, independent of how these sites are handled. In those cases where a full 20 nucleotides were not included within an annotated mRNA, the missing nucleotides were treated as unknown. Additionally, we included two variables based on free energy expressed in units of kcal/mole at 20°C: the estimated free energy of folding for each 41-nucleotide sequence (20 bases 5', the edited/non-edited base, 20 bases 3') and the change in free energy of folding between the non-edited and edited versions of the 41-nucleotide sequence. Free energies of folding were calculated using mfold [ 28 , 29 ] version 3.1 with program parameters except temperature at default values. Finally, we included codon position as a variable, even though the null set had been chosen so non-edited sites had the same distribution of codon position as the edited sites, as shown in Table  3 . Including codon position as a predictor variable allows for possible interactions with other variables. Finally, we created a combined data set to use alongside the species-specific datasets. The combined dataset is the result of combining all edited sites from all three species (there were no observations identical in all predictor variables), and then randomly selecting negative examples from the set of those already chosen for the three individual datasets. Negative examples were chosen to exactly match the positive examples in distribution over both species and codon position. The combined dataset comprises 2,694 observations.
Variable selection
Incomplete annotations in the GenBank sequences required us to algorithmically determine on which strand an edited site fell (the GenBank files sometimes supplied only a position number, with no strand information). The algorithm, implemented in a Perl script, scanned the entire GenBank file and built an in-memory representation of the layout of all genes and coding sequence regions in the genome. The strand with which an edited site was associated could then be determined by consulting the resultant genome map and checking which strand at the edited site contained a gene region. In no case were genes on both strands at an edited site, so strand localization was always unambiguous. In a few cases, however, a gene containing an edited site could not be located, or a site marked as a C-to-U edit did not contain a C in either strand. In these cases, the supposed edited site was eliminated from further consideration. Final numbers of included sites were as follows:  Arabidopsis , 444;  Brassica , 422;  Oryza , 481. In total, 19 edited sites in the GenBank files were not included across all three species.ArabidopsisBrassicaOryzaWe also constructed a set of null observations of cytidines that are not edited to uridines. In constructing a null-set, it is important to ensure that the observations are as alike as possible to the edited observations (differing only in the trait to be measured), or the resulting model may be fictive. Here, our null-set observations were non-edited cytidines chosen at random from within gene regions of the genome. Additionally, we chose cytidines such that the null set had exactly the same distribution of codon positions as did the edited set, because the distribution of edited sites within the three possible positions of a codon is highly non-random with a bias to the first two positions [ 9 ] (Table  3 ).For each observation, we recorded 40 nucleotide state variables: one variable for each of the 20 nucleotides sites 5' and 3' of the edited C (on the same strand). We chose a value of 20 for the number of nucleotides 5' and 3' so as to encompass the entire range of semi-conserved positions previously suggested, the most extreme of which occurs 17 bases 5' of the edited site [ 9 ]. In some cases other edited sites occurred within the 20 nucleotides 5' and 3' of the edited site used as a response variable. In these cases the edited sites as predictor variables were recorded as C. The low frequency of these sites at a particular position with respect to other edited sites results in non-significant effects, independent of how these sites are handled. In those cases where a full 20 nucleotides were not included within an annotated mRNA, the missing nucleotides were treated as unknown. Additionally, we included two variables based on free energy expressed in units of kcal/mole at 20°C: the estimated free energy of folding for each 41-nucleotide sequence (20 bases 5', the edited/non-edited base, 20 bases 3') and the change in free energy of folding between the non-edited and edited versions of the 41-nucleotide sequence. Free energies of folding were calculated using mfold [ 28 , 29 ] version 3.1 with program parameters except temperature at default values. Finally, we included codon position as a variable, even though the null set had been chosen so non-edited sites had the same distribution of codon position as the edited sites, as shown in Table  3 . Including codon position as a predictor variable allows for possible interactions with other variables.Finally, we created a combined data set to use alongside the species-specific datasets. The combined dataset is the result of combining all edited sites from all three species (there were no observations identical in all predictor variables), and then randomly selecting negative examples from the set of those already chosen for the three individual datasets. Negative examples were chosen to exactly match the positive examples in distribution over both species and codon position. The combined dataset comprises 2,694 observations.Data analysis Tree-based statistical models We used the R language for statistical computing [ 30 ], version 1.7.1 to conduct our analyses. Analyses included tree-based statistical models using rpart [ 31 ] and random forests using the FORTRAN implementation of random forest version 3.1 [ 24 , 32 ]. Tree-based statistical models [ 33 ], also known as classification and regression trees (CART) [ 34 ], are generated by recursively creating binary partitions of a dataset. Each partition is based on the value of a single predictor variable chosen to best produce homogeneous collections of a nominal or ordinal response variable (classification) or to best separate low and high values of a continuous response variable (regression). More precisely, the partitions may be considered as questions of the following form: Is the observation x i  ∈  A ? Where  A  is a region of the variable space defined by some criterion of a single predictor variable. Answering such a question for all observations produces two groups: those observations for which the answer is  yes  (those in region  A ) and those for which the answer is  no  (x i  ∉  A , those in  ). Subsequent binary partitioning continues until stopping criteria (variously defined) are met [ 34 ]. The result is a classification or a regression tree: a hierarchical series of data bifurcations that depicts the partition definitions and describes the resulting data subsets defined by each partition. To address concerns about possible over-fitting models to the data we used 10-fold cross-validation and pruned trees to the shortest within 1- SE  of the best tree. We assessed the significance of our tree-based statistical models through permutation where the predictor variables are randomized with respect to the response variable [ 35 ]. The frequency of observing a result value equal to or better than the observed value in 1 × 10 4  permutations is the estimate of the probability associated with the observed result. Random forests If one tree-based statistical model is good, then an ensemble (forest) of appropriately constructed tree models should be even better, which is the principal idea of random forests. A random forest attempts to improve upon a simple tree-based statistical model by generating a collection of such models and using them in aggregate [ 24 , 32 ]. Each model in a random forest is generated from a bootstrap sample of the original dataset, and at each node in each model a search for the best possible split is through a subset of variables selected at random from the bootstrap sample of predictor variables. These randomization steps decrease prediction error through variance reduction resulting from averaging and by decreasing the correlation between individual models in the ensemble [ 36 , 37 ]. Each of our random forest analyses comprised 1 × 10 4  individual models constructed by sub-sampling seven predictor variables at each node. Several model summary statistics were calculated, including sensitivity, which is the proportion of observations correctly identified as edited, specificity, which is the proportion of observations correctly identified as non-edited, and accuracy, which is the total proportion of observations correctly identified. More formally, these definitions are: sensitivity = true positives/ ( true positives  +  false negatives ); specificity = true negatives/ ( true negatives  +  false positives ); and accuracy  = ( true positives  +  true negatives )/ total .
Data analysis
Tree-based statistical models We used the R language for statistical computing [ 30 ], version 1.7.1 to conduct our analyses. Analyses included tree-based statistical models using rpart [ 31 ] and random forests using the FORTRAN implementation of random forest version 3.1 [ 24 , 32 ]. Tree-based statistical models [ 33 ], also known as classification and regression trees (CART) [ 34 ], are generated by recursively creating binary partitions of a dataset. Each partition is based on the value of a single predictor variable chosen to best produce homogeneous collections of a nominal or ordinal response variable (classification) or to best separate low and high values of a continuous response variable (regression). More precisely, the partitions may be considered as questions of the following form: Is the observation x i  ∈  A ? Where  A  is a region of the variable space defined by some criterion of a single predictor variable. Answering such a question for all observations produces two groups: those observations for which the answer is  yes  (those in region  A ) and those for which the answer is  no  (x i  ∉  A , those in  ). Subsequent binary partitioning continues until stopping criteria (variously defined) are met [ 34 ]. The result is a classification or a regression tree: a hierarchical series of data bifurcations that depicts the partition definitions and describes the resulting data subsets defined by each partition. To address concerns about possible over-fitting models to the data we used 10-fold cross-validation and pruned trees to the shortest within 1- SE  of the best tree. We assessed the significance of our tree-based statistical models through permutation where the predictor variables are randomized with respect to the response variable [ 35 ]. The frequency of observing a result value equal to or better than the observed value in 1 × 10 4  permutations is the estimate of the probability associated with the observed result.
Tree-based statistical models
We used the R language for statistical computing [ 30 ], version 1.7.1 to conduct our analyses. Analyses included tree-based statistical models using rpart [ 31 ] and random forests using the FORTRAN implementation of random forest version 3.1 [ 24 , 32 ].Tree-based statistical models [ 33 ], also known as classification and regression trees (CART) [ 34 ], are generated by recursively creating binary partitions of a dataset. Each partition is based on the value of a single predictor variable chosen to best produce homogeneous collections of a nominal or ordinal response variable (classification) or to best separate low and high values of a continuous response variable (regression). More precisely, the partitions may be considered as questions of the following form: Is the observation x i  ∈  A ? Where  A  is a region of the variable space defined by some criterion of a single predictor variable. Answering such a question for all observations produces two groups: those observations for which the answer is  yes  (those in region  A ) and those for which the answer is  no  (x i  ∉  A , those in  ). Subsequent binary partitioning continues until stopping criteria (variously defined) are met [ 34 ]. The result is a classification or a regression tree: a hierarchical series of data bifurcations that depicts the partition definitions and describes the resulting data subsets defined by each partition. To address concerns about possible over-fitting models to the data we used 10-fold cross-validation and pruned trees to the shortest within 1- SE  of the best tree.iAAyesAnoiASEWe assessed the significance of our tree-based statistical models through permutation where the predictor variables are randomized with respect to the response variable [ 35 ]. The frequency of observing a result value equal to or better than the observed value in 1 × 10 4  permutations is the estimate of the probability associated with the observed result.Random forests If one tree-based statistical model is good, then an ensemble (forest) of appropriately constructed tree models should be even better, which is the principal idea of random forests. A random forest attempts to improve upon a simple tree-based statistical model by generating a collection of such models and using them in aggregate [ 24 , 32 ]. Each model in a random forest is generated from a bootstrap sample of the original dataset, and at each node in each model a search for the best possible split is through a subset of variables selected at random from the bootstrap sample of predictor variables. These randomization steps decrease prediction error through variance reduction resulting from averaging and by decreasing the correlation between individual models in the ensemble [ 36 , 37 ]. Each of our random forest analyses comprised 1 × 10 4  individual models constructed by sub-sampling seven predictor variables at each node. Several model summary statistics were calculated, including sensitivity, which is the proportion of observations correctly identified as edited, specificity, which is the proportion of observations correctly identified as non-edited, and accuracy, which is the total proportion of observations correctly identified. More formally, these definitions are: sensitivity = true positives/ ( true positives  +  false negatives ); specificity = true negatives/ ( true negatives  +  false positives ); and accuracy  = ( true positives  +  true negatives )/ total .
Random forests
If one tree-based statistical model is good, then an ensemble (forest) of appropriately constructed tree models should be even better, which is the principal idea of random forests. A random forest attempts to improve upon a simple tree-based statistical model by generating a collection of such models and using them in aggregate [ 24 , 32 ]. Each model in a random forest is generated from a bootstrap sample of the original dataset, and at each node in each model a search for the best possible split is through a subset of variables selected at random from the bootstrap sample of predictor variables. These randomization steps decrease prediction error through variance reduction resulting from averaging and by decreasing the correlation between individual models in the ensemble [ 36 , 37 ]. Each of our random forest analyses comprised 1 × 10 4  individual models constructed by sub-sampling seven predictor variables at each node.Several model summary statistics were calculated, including sensitivity, which is the proportion of observations correctly identified as edited, specificity, which is the proportion of observations correctly identified as non-edited, and accuracy, which is the total proportion of observations correctly identified. More formally, these definitions are:sensitivity = true positives/ ( true positives  +  false negatives );sensitivity = true positives/true positivesfalse negativesspecificity = true negatives/ ( true negatives  +  false positives ); andspecificity = true negatives/true negativesfalse positivesaccuracy  = ( true positives  +  true negatives )/ total .accuracytrue positivestrue negativestotalAuthors' contributions MPC conceived, designed and coordinated the study. DSM carried out the programming and statistical analyses. Both authors wrote and approved the final manuscript.
Authors' contributions
MPC conceived, designed and coordinated the study. DSM carried out the programming and statistical analyses. Both authors wrote and approved the final manuscript.Supplementary Material Additional File 1 Arabidopsis thaliana  data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation. Click here for file Additional File 2 Brassica napus  data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation. Click here for file Additional File 3 Oryza sativa  data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation. Click here for file Additional File 4 Combined data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation. Click here for file
Supplementary Material
Additional File 1
Arabidopsis thaliana  data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation.Arabidopsis thalianadata fileClick here for fileAdditional File 2
Brassica napus  data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation.Brassica napusdata fileClick here for fileAdditional File 3
Oryza sativa  data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation.Oryza sativadata fileClick here for fileAdditional File 4
Combined data file  File is plain text, space delimited. First row is column headings with variable names: edit; + site is edited, - site is not edited; -20 through 20, nucleotide position relative to edited site; cp, codon position; fe, estimated folding energy; dfe, difference in estimated folding energy between pre-edited and edited sequences; and loc, location of focus site (position 0) in GenBank file. Each subsequent line represents a observation.Combined data fileClick here for file


The Icelandic population is now a part of a unique epidemiological study, which has involved investigating the genetic heritage of many of them. The reason that this experiment can be done is because of the remarkable records that exist in Iceland. Not only is there almost complete genealogical information dating back to the 18th century on all current (288,000) and many previous Icelanders (more than 600,000 in total), but in addition the country has an almost complete cancer registry dating from 1955. A company, deCODE Genetics, was set up to mine health-care data in Iceland, and to use it to assess the effect of genetics on health. Initially, the company attracted criticism, with some questioning the ethics of providing access to health-care data for many disease projects to a for-profit company. But the company has been supported by many Icelanders themselves, demonstrated by Icelanders donating blood samples with informed consent for research on multiple diseases, and now the project's scientific value is becoming apparent.One such analysis is the subject of a paper by Laufey Amundadottir and colleagues in this month's  PLoS Medicine  that assesses how much genetic factors contribute to cancer risk across the whole Icelandic population.PLoS MedicineThe paper looked at 27 different types of cancers (all those with more than 200 cases) that had been registered between 1955 and 2002 and analysed the frequency of close and distant relatives also having that cancer, or another kind of cancer. Of the 27 cancers, 16 showed significant “familiality,” and for some this risk even extended to distant (that is, third- to fifth-degree) relatives. The seven cancers with the highest increased familial occurrence both in close and distant relatives were breast, prostate, stomach, lung, colon, kidney, and bladder cancers. And, interestingly, three cancers—stomach, lung, and colon cancer—were also seen more frequently in mates of patients, indicating a shared environmental risk factor. And for some cancers there was a familial association with other cancers, for example, relatives of individuals with stomach, colon, rectal, or endometrial cancer were more likely to have any of these cancers.Cathryn Lewis, the academic editor for the paper comments on the study's strengths. “This level of family relationship and clinical diagnosis is rarely available from interviewing patients and family members. The size of the study (over 600,000 individuals, with 32,000 cancer cases) and the high quality of data enables the authors to detect subtle effects across distant relationships.”How robust are these data, and what do they mean for the biological understanding of cancer? As Lewis says, “Although the current study is impressive in its size and scope, even here, the sample size becomes an issue, with the most convincing results seen in the most common cancers.” Certainly not all the findings are surprising; some rare cancers are already known to be associated with particular genetic defects, and syndromes that predispose to multiple cancers have been described, for example, that of Hereditary Nonpolyposis Colorectal Cancer. Other associations are more intriguing—the cluster of related cancers that include prostate, kidney, and bladder could possibly have a developmental origin, since all arise from the same part of the embryo.So, by highlighting these subtle links, the study's particular value may become apparent: deciding future avenues of investigation in the complex interrelationships that interact to produce cancer.