The LINC complex is found in a wide variety of organisms and is formed by the transluminal interaction between outer- and inner-nuclear-membrane KASH and SUN proteins, respectively. Most extensively studied are SUN1 and SUN2 proteins, which are widely expressed in mammals. Although SUN1 and SUN2 play functionally redundant roles in several cellular processes, more recent studies have revealed diverse and distinct functions for SUN1. While several recent in vitro structural studies have revealed the molecular details of various fragments of SUN2, no such structural information is available for SUN1. Herein, we conduct a systematic analysis of the molecular relationships between SUN1 and SUN2, highlighting key similarities and differences that could lead to clues into their distinct functions. We use a wide range of computational tools, including multiple sequence alignments, homology modeling, molecular docking, and molecular dynamic simulations, to predict structural differences between SUN1 and SUN2, with the goal of understanding the molecular mechanisms underlying SUN1 oligomerization in the nuclear envelope. Our simulations suggest that the structural model of SUN1 is stable in a trimeric state and that SUN1 trimers can associate through their SUN domains to form lateral complexes. We also ask whether SUN1 could adopt an inactive monomeric conformation as seen in SUN2. Our results imply that the KASH binding domain of SUN1 is also inhibited in monomeric SUN1 but through weaker interactions than in monomeric SUN2.