Complex macromolecular systems are ubiquitous in materials science and biology. These systems exhibit fascinating structural and dynamical properties encompassing a broad range of temporal and spatial scales. A macromolecular system's molecular structure and interactions ultimately determine its macroscopic properties. An ongoing and significant challenge is understanding the underlying principles governing the relationships between microscopic behavior and the ensuing properties that emerge on mesoscopic and macroscopic scales.

We apply the integral equation theory of liquids, statistical mechanics, and machine learning to model complex macromolecular systems' equilibrium and time-dependent properties.

I will present some of our ongoing research on identifying the dynamical modes of proteins relevant for their binding to DNA and their function as bound protein-DNA complexes. In addition, I will discuss an application of machine learning to model polymeric systems for environmental applications (e.g., decarbonization). Finally, I will discuss how the coupling between rotational and shape fluctuations of macromolecules may facilitate the self-assembly of protein-DNA complexes, which is relevant to biological processes of gene regulation.