TopologyNet swMATH ID: 41013 Software Authors: Zixuan Cang, Guo-Wei Wei Description: TopologyNet: Topology based deep convolutional 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 entangled geometric complexity and biological complexity. We introduce topology, i.e., element specific persistent homology (ESPH), to untangle geometric complexity and biological complexity. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains crucial biological information via a multichannel image representation. It is able to reveal hidden structure-function relationships in biomolecules. We further integrate ESPH and 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 limitations to deep learning arising from small and noisy training sets, we present a multitask topological convolutional neural network (MT-TCNN). We demonstrate that the present TopologyNet architectures outperform other state-of-the-art methods in the predictions of protein-ligand binding affinities, globular protein mutation impacts, and membrane protein mutation impacts. Homepage: https://arxiv.org/abs/1704.00063 Related Software: Ripser; TDA; PersistenceImages; javaPlex; Dionysus; PHAT; Gudhi; GitHub; jHoles; Perseus; SW1PerS; AGL-Score; CHARMM; JStatCom; TADD; Scikit; PyDEC; SciPy; DioDe; HERMES Cited in: 8 Publications all top 5 Cited by 16 Authors 7 Wei, Guowei 3 Chen, Jiahui 3 Tong, Yiying 3 Zhao, Rundong 2 Cang, Zixuan 1 Bramer, David 1 Grbić, Jelena 1 Munch, Elizabeth 1 Ramamurthy, Karthikeyan Natesan 1 Ribando-Gros, Emily 1 Som, Anirudh 1 Turaga, Pavan K. 1 Wang, Menglun 1 Wang, Rui 1 Wu, Jie 1 Xia, Kelin all top 5 Cited in 6 Serials 2 Foundations of Data Science 1 Bulletin of Mathematical Biology 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied and Computational Topology 1 Computational and Mathematical Biophysics 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 10 Fields 6 Algebraic topology (55-XX) 5 Biology and other natural sciences (92-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) Citations by Year