In computational structural biology, predicting metal-binding sites and their corresponding metal types is challenging due to the complexity of protein structures and interactions. Conventional sequence- and structure-based prediction approaches cannot capture the complex evolutionary relationships driving these interactions to facilitate understanding, while recent co-evolution-based approaches do not fully consider the entire structure of the co-evolved residue network. In this paper, we introduce MBGNN (Metal-Binding Graph Neural Network) that utilizes the entire co-evolved residue network and effectively captures the complex dependencies within protein structures via graph neural networks to enhance the prediction of co-evolved metal-binding residues and their associated metal types. Experimental results on a public dataset show that MBGNN outperforms existing co-evolution-based metal-binding prediction methods, and it is also competitive against recent sequence-based methods, showing the potential of integrating co-evolutionary insights with advanced machine learning to deepen our understanding of protein-metal interactions. The MBGNN code is publicly available at https://github.com/SRastegari/MBGNN.

We have measured the dissimilarities among several printed characters of a single page in the Gutenberg 42-line bible and we prove statistically the existence of several different matrices from which the metal types where constructed. This is in contrast with the prevailing theory, which states that only one matrix per character was used in the printing process of Gutenberg's greatest work. The main mathematical tool for this purpose is cluster analysis, combined with a statistical test for outliers. We carry out the research with two letters, i and a. In the first case, an exact clustering method is employed; in the second, with more specimens to be classified, we resort to an approximate agglomerative clustering method. The results show that the letters form clusters according to their shape, with significant shape differences among clusters, and allow to conclude, with a very small probability of error, that indeed the metal types used to print them were cast from several different matrices. Mathematics Subject Classification: 62H30