Conditioned free-energy density of proteins using unbalanced solutions to constraint satisfaction problems
For computational biology, this provides a new method to analyze protein free-energy landscapes, though the application is limited to a single protein.
The paper reduces computing the log-partition function of conditioned inhomogeneous Curie-Weiss spin Hamiltonians to an unbalanced 2-to-1 norm computation and provides a polynomial-time SDP algorithm with a lower bound proof. Applied to Ubiquitin, it explores backbone conformations and identifies flexible regions while preserving native secondary structure.
We show that computing the log-partition function (free-energy) of conditioned inhomogeneous Curie--Weiss spin Hamiltonians reduces to an unbalanced $2 \to 1$ norm computation, and design a polynomial-time SDP algorithm for this problem with a lower bound proof for the amount of unbalance achieved. Applied to the protein Ubiquitin, the framework starts from a known crystal structure, explores alternative backbone conformations across the free-energy landscape, and identifies flexible regions of the protein while preserving its native secondary structure.