Recent advances in long-range Hi-C contact mapping have revealed the importance of the 3D structure of chromosomes in gene expression. A current challenge is to identify the key molecular drivers of this 3D structure. Several genomic features, such as architectural proteins and functional elements, were shown to be enriched at topological domain borders using classical enrichment tests. Here we propose multiple logistic regression to identify those genomic features that positively or negatively influence domain border establishment or maintenance. The model is flexible, and can account for statistical interactions among multiple genomic features. Using both simulated and real data, we show that our model outperforms enrichment test and non-parametric models, such as random forests, for the identification of genomic features that influence domain borders. Using Drosophila Hi-C data at a very high resolution of 1 kb, our model suggests that, among architectural proteins, BEAF-32 and CP190 are the main positive drivers of 3D domain borders. In humans, our model identifies well-known architectural proteins CTCF and cohesin, as well as ZNF143 and Polycomb group proteins as positive drivers of domain borders. The model also reveals the existence of several negative drivers that counteract the presence of domain borders including P300, RXRA, BCL11A and ELK1.