Machine Learning for Enzyme Promiscuity

With the discovery of an increasing number of catalytically promiscuous enzymes, which are capable of catalyzing multiple reactions, the traditional view of enzymes as highly specific proteins has been brought into question. The significant implications of protein promiscuity for the theory of enzyme evolution suggest that this inherent feature can be utilized as the seed for engineering new functions in biotechnology and synthetic biology as well as in drug design. Therefore, understanding protein promiscuity is becoming even more important as it provides new insights into the evolutionary process that has led to such vast functional diversity. While there have been numerous efforts devoted to recognizing the determinants of promiscuity, till date, this pertinent question regarding the distinctions between specialized enzymes and promiscuous enzymes has remained unanswered. As an in silico approach, in this thesis, we attempt to find a predictive model which can accurately classify unseen proteins into catalytically promiscuous and non-promiscuous. To this end, we exploit different representations and properties of proteins, and adopt different computational approaches accordingly. The role of proteins sequences as indicators of promiscuity is investigated by means of the BLAST algorithm as well as string kernels. Additionally, to validate the interplay between proteins' three-dimensional structures and their promiscuous behaviors, we employ a novel method which is modeling the topological details of proteins as graphs. Graph kernel functions are then applied to measure the structural similarities between the 3D structures of proteins. The classification is performed using SVM as a kernel-based method. The results indicate that proteins' sequences have limited bearings on promiscuity. Conversely, proteins' 3D structures can reliably predict whether a protein has promiscuous activities with an accuracy of 96%. Our best results are achieved using the Weisfeiler-Lehman subtree graph kernel and the secondary structure information of proteins

On Filter Size in Graph Convolutional Networks

Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional filters over multi-dimensional tensors. In particular, we derive a simple, efficient and effective way to introduce a hyper-parameter on graph convolutions that influences the filter size, i.e. its receptive field over the considered graph. We show with experimental results on real-world graph datasets that the proposed graph convolutional filter improves the predictive performance of Deep Graph Convolutional Networks.Comment: arXiv admin note: text overlap with arXiv:1811.0693

Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on many tasks, their foundation on pairwise interaction networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art (SOTA) performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs