TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions

Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/Author summary: The predictions of biomolecular functions and properties from biomolecular structures are of fundamental importance in computational biophysics. The structural and biological complexities of biomolecules and their interactions hinder successful predictions. Machine learning has become an important tool for such predictions. Recent advances in deep learning architectures, particularly convolutional neural network (CNN), have profoundly impacted a number of disciplines, such as image classification and voice recognition. Though CNN can be directly applied to molecular sciences by using a three-dimensional (3D) image-like brute-force representation, it is computationally intractable when applied to large biomolecules and large datasets. We propose a topological strategy to significantly reduce the structural and biological complexity of biomolecules and provide an efficient topology based CNN architecture. Element-specific persistent homology, a new algebraic topology, has been developed to cast biomolecules in a multichannel image-like representation suitable for CNN. The power of the proposed topology based neural network (TopologyNet) is further enhanced by auxiliary descriptors and a multi-task deep learning architecture. It has been demonstrated that TopologyNet framework outperforms other methods in the predictions of protein-ligand binding affinities and mutation induced protein stability changes.