Topological potentials guiding protein self-assembly

The simulated assembly of molecular building blocks into functional complexes is central to computational biology and materials science. Protein-assembly simulations, driven by short-range nonpolar interactions, can in principle reach their biologically correct structures, but rugged energy landscapes often trap simulations in non-functional local minima. We introduce a long-range topological potential, quantified by weighted total persistence, and combine it with the morphometric approach to solvation free energy. Across four protein systems, this combination increases assembly success rates by up to sixteen-fold and enables assembly in cases that otherwise fail. Unlike previous topology-based approaches, our method uses topological measures as an active energetic bias rather than a descriptive tool. Depending only on atom geometry, the method extends in principle to other self-assembling systems, offering a general strategy for overcoming kinetic barriers in molecular simulations.Author summary: We developed a new computational method that helps simulate how proteins assemble into functional complexes. Proteins often need to come together in precise arrangements to function, but computer simulations of this process frequently get stuck in incorrect configurations due to the complexity of the energy landscape. Our key insight is that tools from computational topology, specifically persistent homology, can be used not just to analyze molecular shapes after the fact, but as an active guiding force within the simulation itself. We define a topological potential that captures shape information over long distances, complementing a geometric model of solvation free energy that drives assembly at close contact. When we combine both potentials, the topological term acts as a funnel that pulls protein subunits into roughly the right arrangement, while the geometric term handles precise docking. We tested this on four different protein systems, including components of the tobacco mosaic virus, hepatitis B, SARS-CoV-2, and the human immune system, and found that our combined approach dramatically improves assembly success rates, increasing them by up to sixteen-fold compared to using the geometric model alone.