The folding structure of the DNA molecule combined with helper molecules, also referred to as the chromatin, is highly relevant for the functional properties of DNA. The chromatin structure is largely determined by the underlying primary DNA sequence, though the interaction is not yet fully understood. In this paper we develop a convolutional neural network that takes an image-representation of primary DNA sequence as its input, and predicts key determinants of chromatin structure. The method is developed such that it is capable of detecting interactions between distal elements in the DNA sequence, which are known to be highly relevant. Our experiments show that the method outperforms several existing methods both in terms of prediction accuracy and training time. DNA is perceived as a sequence over the letters {A,C,G,T }, the alphabet of nucleotides. This sequence constitutes the code that acts as a blueprint for all processes taking place in a cell. But beyond merely reflecting primary sequence, DNA is a molecule, which implies that DNA assumes spatial structure and shape. The spatial organization of DNA is achieved by integrating ("recruiting") other molecules, the histone proteins, that help to assume the correct spatial configuration. The combination of DNA and helper molecules is called chromatin; the spatial configuration of the chromatin, finally, defines the functional properties of local areas of the DNA BID9 .Chromatin can assume several function-defining epigenetic states, where states vary along the genome BID12 . The key determinant for spatial configuration is the underlying primary DNA sequence: sequential patterns are responsible for recruiting histone proteins and their chemical modifications, which in turn give rise to or even define the chromatin states. The exact configuration of the chromatin and its interplay with the underlying raw DNA sequence are under active research. Despite many enlightening recent findings (e.g. BID6 The EN-CODE Project Consortium, 2012; BID11 , comprehensive understanding has not yet been reached. Methods that predict chromatin related states from primary DNA sequence are thus of utmost interest. In machine learning, many prediction methods are available, of which deep neural networks have recently been shown to be promising in many applications BID17 . Also in biology deep neural networks have been shown to be valuable (see BID3 for a review).Although DNA is primarily viewed as a sequence, treating genome sequence data as just a sequence neglects its inherent and biologically relevant spatial configuration and the resulting interaction between distal sequence elements. We hypothesize that a deep neural network designed to account for long-term interactions can improve performance. Additionally, the molecular spatial configuration of DNA suggests the relevance of a higher-dimensional spatial representation of DNA. However, due to the lack of comprehensive understanding with respect to the structure of the chromatin, sensible suggestions for such higher-dimensional representations of DNA do not exist.One way to enable a neural net to identify long-term interactions is the use of fully connected layers. However, when the number of input nodes to the fully connected layer is large, this comes with a large number of parameters. We therefore use three other techniques to detect long-term interactions . First, most convolutional neural networks (CNNs) use small convolution filters. Using larger filters already at an early stage in the network allows for early detection of long-term interactions without the need of fully connected layers with a large input. Second, a deep network similar to the ResNet BID14 or Inception BID27 network design prevents features found in early layers from vanishing. Also, they reduce the size of the layers such that the final fully connected layers have a smaller input and don't require a huge number of parameters. Third, we propose a novel kind of DNA representation by mapping DNA sequences to higher-dimensional images using space-filling curves. Space-filling curves map a 1-dimensional line to a 2-dimensional space by mapping each element of the sequence to a pixel in the 2D image. By doing so, proximal elements of the sequence will stay in close proximity to one another, while the distance between distal elements is reduced.The space-filling curve that will be used in this work is the Hilbert curve which has several advantages. (i): [Continuity] Hilbert curves optimally ensure that the pixels representing two sequence elements that are close within the sequence are also close within the image BID4 BID1 . (ii): [Clustering property] Cutting out rectangular subsets of pixels (which is what convolutional filters do) yields a minimum amount of disconnected subsequences BID20 . (iii): If a rectangular subimage cuts out two subsequences that are disconnected in the original sequence, chances are maximal that the two different subsequences are relatively far apart (see our analysis in Appendix A).The combination of these points arguably renders Hilbert curves an interesting choice for representing DNA sequence as two-dimensional images. (i) is a basic requirement for mapping short-term sequential relationships, which are ubiquitous in DNA (such as codons, motifs or intron-exon structure).(ii) relates to the structure of the chromatin, which -without all details being fully understood -is tightly packaged and organized in general. Results from BID10 indicate that when arranging DNA sequence based on Hilbert curves, contiguous areas belonging to identical chromatin states cover rectangular areas. In particular, the combination of (i) and (ii) motivate the application of convolutional layers on Hilbert curves derived from DNA sequence: rectangular subspaces, in other words, submatrices encoding the convolution operations, contain a minimum amount of disconnected pieces of DNA. (iii) finally is beneficial insofar as long-term interactions affecting DNA can also be mapped. This in particular applies to so-called enhancers and silencers, which exert positive ( enhancer) or negative (silencer) effects on the activity of regions harboring genes, even though they may be far apart from those regions in terms of sequential distance. In this paper we developed a CNN that outperforms the state-of-the-art for prediction of epigenetic states from primary DNA sequence. Indeed, our methods show improved prediction accuracy and training time compared to the currently available chromatin state prediction methods from Pahm TAB1 in BID15 . In the splice dataset, Seq-CNN performed best when using 4-mers, while for HCNN and seq-HCNN 1-mers yielded the best performance.results Figure 4 : HCNN with different mapping strategies by BID21 and thus yields a huge number of parameters in the fully connected layer. In HCNN on the other hand the number of nodes is strongly reduced before introducing a fully connected layer. Third, the use of a two-dimensional input further enhances the model's capabilities of incorporating long-term interactions.We showed that seq-HCNN and HCNN are not only capable of predicting chromatin state, but can also predict the presence or absence of splice-junctions in DNA subsequences. This suggests that our approach could be useful for DNA sequence classification problems in general.Hilbert curves have several properties that are desirable for DNA sequence classification. The intuitive motivation for the use of Hilbert curves is supported by good results when comparing Hilbert curves to other space-filling curves. Additionally, Hilbert curves have previously been shown to be useful for visualization of DNA sequences BID2 ).The main limitation of Hilbert curves is their fixed length, which implies that the generated image contains some empty spaces. These spaces consume computation resources; nevertheless, the 2D representation still yields reduced training times compared to the 1D-sequence representation, presumably due to the high degree of optimization for 2D inputs present in standard CNN frameworks.Given that a substantial part of the improvements in performance rates are due to our novel architecture, we plan on investigating the details of how components of the architecture are intertwined with improvements in prediction performance in more detail. We also plan to further investigate why Hilbert curves yield the particular advantages in terms of robustness and false discovery control we have observed here.
A method to transform DNA sequences into 2D images using space-filling Hilbert Curves to enhance the strengths of CNNs
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