Use of machine learning algorithms to classify binary protein sequences as highly-designable or poorly-designable

<p>Abstract</p> <p>Background</p> <p>By using a standard Support Vector Machine (SVM) with a Sequential Minimal Optimization (SMO) method of training, Naïve Bayes and other machine learning algorithms we are able to distinguish between two classes of protein sequences: those folding to highly-designable conformations, or those folding to poorly- or non-designable conformations.</p> <p>Results</p> <p>First, we generate all possible compact lattice conformations for the specified shape (a hexagon or a triangle) on the 2D triangular lattice. Then we generate all possible binary hydrophobic/polar (H/P) sequences and by using a specified energy function, thread them through all of these compact conformations. If for a given sequence the lowest energy is obtained for a particular lattice conformation we assume that this sequence folds to that conformation. Highly-designable conformations have many H/P sequences folding to them, while poorly-designable conformations have few or no H/P sequences. We classify sequences as folding to either highly – or poorly-designable conformations. We have randomly selected subsets of the sequences belonging to highly-designable and poorly-designable conformations and used them to train several different standard machine learning algorithms.</p> <p>Conclusion</p> <p>By using these machine learning algorithms with ten-fold cross-validation we are able to classify the two classes of sequences with high accuracy – in some cases exceeding 95%.</p

Sizes of pentagonal clusters in fullerenes

Stability and chemistry, both exohedral and endohedral, of fullerenes are critically dependent on the distribution of their obligatory 12 pentagonal faces. It is well known that there are infinitely many IPR-fullerenes and that the pentagons in these fullerenes can be at an arbitrarily large distance from each other. IPR-fullerenes can be described as fullerenes in which each connected cluster of pentagons has size 1. In this paper we study the combinations of cluster sizes that can occur in fullerenes and whether the clusters can be at an arbitrarily large distance from each other. For each possible partition of the number 12, we are able to decide whether the partition describes the sizes of pentagon clusters in a possible fullerene, and state whether the different clusters can be at an arbitrarily large distance from each other. We will prove that all partitions with largest cluster of size 5 or less can occur in an infinite number of fullerenes with the clusters at an arbitrarily large distance of each other, that 9 partitions occur in only a finite number of fullerene isomers and that 15 partitions do not occur at all in fullerenes