Conditioned free-energy density of proteins using unbalanced solutions to constraint satisfaction problems

• URL: http://arxiv.org/abs/2606.01329v1
• Date: Sun, 31 May 2026 16:31:16 GMT
• Title: Conditioned free-energy density of proteins using unbalanced solutions to constraint satisfaction problems
• Abstract summary: We show that computing the log-partition function (free-energy) of conditioned ingeneous Curie-We-iss spin Hamiltonians reduces to an unbalanced $2 to 1$ norm, and design a new algorithm for this problem.<n> Applied to the protein Ubiquitin, the framework starts from a known crystal structure, explores alternative backbones, and identifies flexible regions of the protein.
• Score: 1.4146420810689422
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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