Computational Mathematics: Biomolecular and Biophysical Inference

Working at the intersection of statistical mechanics, machine learning, and structural biology, we develop rigorous frameworks to extract biophysical understanding from molecular simulations and noisy and incomplete data.

This group is a collaboration between the Center for Computational Mathematics and the Center for Computational Biology.

Biomolecules carry out their functions by continuously exploring a landscape of conformational states, ranging from stable, highly populated states to rare, transient states that are often functionally essential. Quantifying the populations of these states and the kinetics of transitions between them is central to understanding the molecular mechanisms of biological function. Single-molecule and single-particle techniques, such as cryo-electron microscopy and force spectroscopy, provide direct access to these distributions by recording individual molecules rather than ensemble averages. However, the resulting data are high-dimensional, noisy, and only indirectly related to the underlying structural ensemble, making their interpretation challenging.

A central goal of this team is to develop rigorous statistical and computational frameworks that infer biomolecular structure, conformational populations, and kinetics from such individual measurements. Rather than treating simulation and experiment as separate approaches, we integrate them within unified inference frameworks, using physics-based simulations as prior models that are refined against single-molecule data. This combination enables quantitative, physically interpretable descriptions of biomolecular properties with well-defined uncertainties.

Particular areas of interest include:

• Statistical Biophysics 
• Inference for Biophysics
• Molecular Simulations 
• Cryo-Electron Microscopy 
• Single-Molecule Force Spectroscopy
• Simulation-Based Inference

We have strong collaborations with members of the Center for Computational Biology and the Initiative for Computational Catalysis, who work on molecular simulations and/or cryo-electron microscopy.

Together with researchers in the Center for Computational Mathematics, we are part of the Collaboration On Molecular Physics and Sampling Strategies (COMPASS).