# Exploiting Sparse Statistics for a Sequence-Based Prediction of the Effect of Mutations
## 4 Discussion  
Motivated by the success of the sequence-based predictions for the foldability of an AA sequence using statistics of triplets and quadruplets [2] the present work examined the use of longer \(n\)-tuplets. Since for longer \(n\)-tuplets the statistics gets progressively sparser the treatment of missing or low-quality statistics needed newer approaches.  
The quality of the statistics over pentuplets was the closest to the quality of the triplet and quadruplets statistics so an attempt was made to use them for foldability prediction. As a warning sign that the missing information has significant effect, the score distributions of the two kinds of randomly generated sets were very different and, counterintuitively, the distribution of the AA-propensity based set was more different from the PDB set than distribution of the uniform AA distribution based set. While the predictions on random sets improved, the prediction on the new PDB set worsened, especially when the RU reference set was used.  
The high quality of the pentuplets predictions on the randomly generated sets suggested a combination of the quadruplet and pentuplets prediction. It was found that if the quadruplet predictions were modified with the pentuplets prediction using the RU reference distribution, the quality of predictions on the random sets remained at the quadruplet level but on the new PDB set it improved significantly. This combination was suggested to be an improvement over the quadruplet-based predictions.  
The samples of hextuplets and heptuplets were way too sparse to give estimates of probabilities. Thus a score using only simple counts was developed and used for a different purpose, that of predicting if a mutation increased the stability of a protein or not.  
The prediction using pentuplet, hextuplet and heptuplet statistics were all found to predict the stability change direction of \(\sim\)70% of the mutations examined. Limiting predictions to mutations where more than one \(n\)-tuplets gave the same prediction slightly improved the prediction accuracy: the best prediction accuracy (73.4%) was obtained when pentuplets, hextuplets and heptuplets were combined. While this was still rather weak, given the minimal computing expense involved, especially in comparison to the computational cost of free-energy simulations, it could be helpful in screening a large set of putative mutations for experimental tests.  
If Reference [2] the predictions were based on the statistics of two single properties, the distributions of AA triplets and quadruplets. Several other properties showed differences between the PDB set and the randomly generated sets but not used for foldability predictions as the differences were smaller. The present work showed that some combination of scores resulted in improved prediction accuracy. Future work is planned to find ways of incorporating the statistics so far ignored to further enhance the accuracy of foldability prediction.  
This research received no external funding.  
This work was supported in part through the computational resources and staff expertise provided by the Department of Scientific Computing at the Icahn School of Medicine at Mount Sinai.  
The author declares no conflict of interest.