Learning Topological Representations of Protein Structure and Dynamics

Modern protein representation models support tasks such as enzyme design and drug discovery, but their reliance on static data such as sequence and native structure limits their ability to capture the conformational dynamics that drive protein function. We investigate whether persistent homology (PH) can provide descriptors shared across diverse proteins that retain global structure, fine-grained conformational variability, and kinetically relevant information without large-scale pretraining. We introduce the masked Flood complex, i.e., an adaptation of a recently proposed simplicial complex construction, that incorporates domain knowledge to emphasize inter-residue structure at low computational cost. We then use it to compute PH on molecular dynamics (MD) sampled structures, vectorize the persistence diagrams into a shared coordinate system, and probe the capacity of these representations in terms of the aforementioned aspects. To assess the amount of kinetic information, we learn low-dimensional embeddings from time-lagged observations and evaluate Markov state models (MSMs) estimated from them. Using these MSMs to guide training of the recent marsfm generative framework improves several ensemble statistics relative to the original model. After finetuning on lower-temperature MD data and adapting the sampling procedure, the resulting model also shows promising transfer to fast folding proteins.