BACKGROUND
understanding the relationship between protein sequence and 3d structure is one of the most important research tasks in both biology and bioinformatics researches.
based on many biochemical experiments, it is believed that the sequence is the sole determinate in a polypeptide's structural conformation.
this means all the information that is necessary to specify protein interaction sites is embedded into the polypeptide's amino acid sequence  <cit> .
in order to discover the protein sequence-to-structure relationship, han and baker used the k-means clustering algorithm to produce high quality protein clusters from protein sequence frequency profiles  <cit> .
subsequently, they used the sequence clusters  <cit>  combined with hidden markov model   <cit>  to predict local protein structures.
in their work, the clustering algorithm plays the central role in relating protein sequences to local structures.
however, the conventional clustering algorithms assume that the distance between data points can be calculated with exact precision.
while the distance function is not well characterized, this approach may not reveal the sequence-to-structure relationship efficiently  <cit> .
support vector machines   <cit>  has proven their value in various research domains.
svm apply the soft margin idea to allow mislabelled examples for maximization the margin; therefore, svm has the ability to handle the non-linear classification by implicitly mapping input samples into a higher dimension for maximum-margin hyperplane generation.
under this point of view, svm may be more efficient to discover the non-linear sequence-to-structure relationship than the k-means clustering algorithm  <cit> .
nevertheless, due to the high computational cost of svm, it is not favourable for large datasets  <cit> .
it is almost impossible to model a svm over half a million data segments, which are then used to generate protein sequence recurring patterns.
as a result, svms combined with granular computing might be a key step to uncover the secret behind the sequence-to-structure relationship.
by using the divide-and-conquer principle, granular computing is able to divide a complex data-mining problem into a series of smaller and computationally simpler problems  <cit> .
in this paper, we explain how to merge the power of svm and granule computing to uncover the hidden information between the relationship of sequence and structure.
a detailed report on local protein structure prediction results based on sequence information is also provided.
RESULTS
super granule support vector machines
to perform the true merit of the granular computing combined with the power of the svm, we propose a new computational model, the super granule support vector machines , in this paper.
in the super gsvm, the large dataset is first softly separated into several information granules by the fuzzy c-means clustering and then succeeded by the greedy k-means clustering for sequence cluster generation on each information granule.
after that, one ranking-svm is built for each sequence cluster to learn the non-linear sequence-to-structure relationship in each cluster.
each ranking-svm serves two major purposes:  <dig>  extracting the sequence cluster to generate higher quality protein recurring pattern information;  <dig>  predicting the protein local 3d structure.
figure  <dig> is the sketch of super gsvm.
protein local 3d structure prediction
in our previous work  <cit> , by using the fgk model , we obtained  <dig> out of  <dig> high quality sequence clusters using a window size of nine from more than half million sequence segments generated from protein sequence profiles.
in this work, we further extract these  <dig> sequence clusters and improve the high quality cluster number from  <dig> to  <dig> by using the super gsvm model .
then we divide these  <dig> sequence clusters into three groups  based on their secondary structural similarity and use these information with a trained ranking-svm model to predict protein local 3d structure from the primary structure  information.
since the different distance thresholds and the different clustering groups generate distinct prediction accuracy, table  <dig> shows a detailed report to indicate the relation between these two factors.
unsurprisingly, the excellent clustering groups always have better prediction accuracy.
when the distance threshold is set to  <dig>  the highest prediction accuracy is achieved, which is almost 72%, based on the criteria of the average difference on dmrmsd being less than  <dig>  Å. with more restrict  distance threshold, the prediction usually performs better; however, the prediction coverage  is getting lower.
it is also the reason why we do not show any prediction accuracy with the distance threshold less than  <dig>  no meaningful prediction coverage can be provided.
experimental results show that if we use excellent group of clusters, we are able to predict around  <dig> %  sequence segments with 70% accuracy when the distance threshold is set to  <dig>  the analysis between distance threshold and prediction coverage is shown in table  <dig>  under smaller distance threshold, the difference of prediction coverage between three clustering groups is not distinct.
but since fair cluster group contains larger number of clusters  than good cluster group  and excellent cluster group , while the distance threshold increases, the difference of prediction coverage becomes more obvious.
in this work, we use super gsvm to generate and extract sequence clusters.
we divided the whole training dataset into  <dig> information granules, the second row shows the number of clusters in each information granule .
the table also show the number of clusters belong to excellent , good , and fair  clusters before and after the super gsvm extraction.
discussion
we try to discover the sequence-to-structure relation by predicting protein 3d information, which is mainly focus on dmrmsd, from purely sequence knowledge.
some other tertiary structure knowledge such as torsion angle  <cit>  can also be adapted in our future work as an additional source of 3d structural information.
besides, since the ranking-svm also gives ranking information on the target examples instead of simply a yes or no, it is highly possible to develop a strong voting mechanism to generate better prediction accuracy results.
CONCLUSIONS
in this work, we propose a super gsvm model to discover the hidden protein sequence-to-structure information.
we cluster on sequence profiles to find the recurring sequence patterns and evaluate the clusters by secondary structure similarity.
we then build a ranking-svm for each cluster to improve the secondary structural similarity.
finally, based on the sequence clusters and the corresponding ranking-svms, we predict the tertiary structure of the testing sequences.
if the sequence similarity between the testing segment and the existing cluster is verified, we predict the 3d structure of the testing segment should be similar to the representative 3d structure of the sequence cluster.
no tertiary structure information is involved in the training process; it is how we carry out the merit of discovering the relation between primary structure and tertiary structure.
although the prediction accuracy is not yet perfect, we open a new door to discovering protein sequence-to-structure information and believe many future works can be applied on our research methods to uncover this mystery.
the proposed super gsvm model is also favourable to many other scientific areas with huge amount of datasets.

 understanding the relationship between protein sequence and 3d structure is one of the most important research tasks in both biology and bioinformatics researches. based on many biochemical experiments, it is believed that the sequence is the sole determinate in a polypeptide's structural conformation. this means all the information that is necessary to specify protein interaction sites is embedded into the polypeptide's amino acid sequence. in order to discover the protein sequence-to-structure relationship, han and baker used the k-means clustering algorithm to produce high quality protein clusters from protein sequence frequency profiles. subsequently, they used the sequence clusters combined with hidden markov model to predict local protein structures. in their work, the clustering algorithm plays the central role in relating protein sequences to local structures. however, the conventional clustering algorithms assume that the distance between data points can be calculated with exact precision. while the distance function is not well characterized, this approach may not reveal the sequence-to-structure relationship efficiently. support vector machines has proven their value in various research domains. svm apply the soft margin idea to allow mislabelled examples for maximization the margin; therefore, svm has the ability to handle the non-linear classification by implicitly mapping input samples into a higher dimension for maximum-margin hyperplane generation. under this point of view, svm may be more efficient to discover the non-linear sequence-to-structure relationship than the k-means clustering algorithm. nevertheless, due to the high computational cost of svm, it is not favourable for large datasets. it is almost impossible to model a svm over half a million data segments, which are then used to generate protein sequence recurring patterns. as a result, svms combined with granular computing might be a key step to uncover the secret behind the sequence-to-structure relationship. by using the divide-and-conquer principle, granular computing is able to divide a complex data-mining problem into a series of smaller and computationally simpler problems. in this paper, we explain how to merge the power of svm and granule computing to uncover the hidden information between the relationship of sequence and structure. a detailed report on local protein structure prediction results based on sequence information is also provided.  super granule support vector machines to perform the true merit of the granular computing combined with the power of the svm, we propose a new computational model, the super granule support vector machines, in this paper. in the super gsvm, the large dataset is first softly separated into several information granules by the fuzzy c-means clustering and then succeeded by the greedy k-means clustering for sequence cluster generation on each information granule. after that, one ranking-svm is built for each sequence cluster to learn the non-linear sequence-to-structure relationship in each cluster. each ranking-svm serves two major purposes: extracting the sequence cluster to generate higher quality protein recurring pattern information; predicting the protein local 3d structure. figure is the sketch of super gsvm. protein local 3d structure prediction in our previous work, by using the fgk model, we obtained out of high quality sequence clusters using a window size of nine from more than half million sequence segments generated from protein sequence profiles. in this work, we further extract these sequence clusters and improve the high quality cluster number from to by using the super gsvm model. then we divide these sequence clusters into three groups based on their secondary structural similarity and use these information with a trained ranking-svm model to predict protein local 3d structure from the primary structure information. since the different distance thresholds and the different clustering groups generate distinct prediction accuracy, table shows a detailed report to indicate the relation between these two factors. unsurprisingly, the excellent clustering groups always have better prediction accuracy. when the distance threshold is set to the highest prediction accuracy is achieved, which is almost 72%, based on the criteria of the average difference on dmrmsd being less than Å. with more restrict distance threshold, the prediction usually performs better; however, the prediction coverage is getting lower. it is also the reason why we do not show any prediction accuracy with the distance threshold less than no meaningful prediction coverage can be provided. experimental results show that if we use excellent group of clusters, we are able to predict around % sequence segments with 70% accuracy when the distance threshold is set to the analysis between distance threshold and prediction coverage is shown in table under smaller distance threshold, the difference of prediction coverage between three clustering groups is not distinct. but since fair cluster group contains larger number of clusters than good cluster group and excellent cluster group, while the distance threshold increases, the difference of prediction coverage becomes more obvious. in this work, we use super gsvm to generate and extract sequence clusters. we divided the whole training dataset into information granules, the second row shows the number of clusters in each information granule. the table also show the number of clusters belong to excellent, good, and fair clusters before and after the super gsvm extraction. discussion we try to discover the sequence-to-structure relation by predicting protein 3d information, which is mainly focus on dmrmsd, from purely sequence knowledge. some other tertiary structure knowledge such as torsion angle can also be adapted in our future work as an additional source of 3d structural information. besides, since the ranking-svm also gives ranking information on the target examples instead of simply a yes or no, it is highly possible to develop a strong voting mechanism to generate better prediction accuracy results.  in this work, we propose a super gsvm model to discover the hidden protein sequence-to-structure information. we cluster on sequence profiles to find the recurring sequence patterns and evaluate the clusters by secondary structure similarity. we then build a ranking-svm for each cluster to improve the secondary structural similarity. finally, based on the sequence clusters and the corresponding ranking-svms, we predict the tertiary structure of the testing sequences. if the sequence similarity between the testing segment and the existing cluster is verified, we predict the 3d structure of the testing segment should be similar to the representative 3d structure of the sequence cluster. no tertiary structure information is involved in the training process; it is how we carry out the merit of discovering the relation between primary structure and tertiary structure. although the prediction accuracy is not yet perfect, we open a new door to discovering protein sequence-to-structure information and believe many future works can be applied on our research methods to uncover this mystery. the proposed super gsvm model is also favourable to many other scientific areas with huge amount of datasets. 
the satisfactory prediction results show the super gsvm model generates decent protein sequence clusters and has the ability to capture the hidden sequence-to-structure information. understanding the relationship between the protein sequence and the 3d structure is a major research area in bioinformatics. in this paper, we propose a super granule support vector machine model to obtain the high quality protein sequence motifs and to predict local tertiary structure information based on purely sequence information. the prediction of complete protein tertiary structure based only on sequence information is still an impractical work.
 understanding the relationship between the protein sequence and the 3d structure is a major research area in bioinformatics. the prediction of complete protein tertiary structure based only on sequence information is still an impractical work. this paper aims at revealing the hidden knowledge of the sequence motifs and the local tertiary structure.  in this paper, we propose a super granule support vector machine model to obtain the high quality protein sequence motifs and to predict local tertiary structure information based on purely sequence information.  the proposed model overcomes the innate shortcoming of using the svm on such a large data set, which is the inherent computational complexity involved in training support vectors for huge datasets including half million of samples. the satisfactory prediction results show the super gsvm model generates decent protein sequence clusters and has the ability to capture the hidden sequence-to-structure information. this model also has a strong potential in the application of svms on other research areas with huge datasets. 20- february sixth annual mcbios conference. transformational bioinformatics: delivering value from genomes starkville, ms, usa 