Entropy-controlled free energy models for protein folding under cellular-like conditions: a conceptual framework

Ioan-Matei Rusu¹, Juliana Margineanu^{1, 2}, Stefan-Rares Maxim¹, Radu Magop¹, Ioana Creanga-Murariu¹, Ionel-Bogdan Tamba^{1 *}

¹ Prof. Ostin C. Mungiu Advanced Research and Development Center for Experimental Medicine – CEMEX, Grigore T. Popa University of Medicine and Pharmacy, Iasi, Romania
² Alexandru Ioan Cuza University, Iasi, Romania
* Correspondence to: Ionel-Bogdan Tamba, Prof. Ostin C. Mungiu Advanced Research and Development Center for Experimental Medicine – CEMEX, Grigore T. Popa University of Medicine and Pharmacy, 16 Universitatii Str., 700115, Iasi, Romania. E-mail: bogdan.tamba@umfiasi.ro

Abstract

Understanding how cellular conditions modulate protein folding requires models that make internal entropy and environmental control parameters explicit. Here, we propose a conceptual and computational framework in which the Helmholtz free energy of folding is decomposed into an internal entropy term that is resolved by local constraints (hydrogen bonds, hydrophobic contacts, salt bridges) and an external contribution controlled by crowding agents and osmolytes. We treat the cellular environment as a control vector whose components enter the free energy through phenomenological corrections informed by scaled-particle and preferential-interaction theories. On top of this thermodynamic structure, we introduce a simple information-geometric viewpoint, using the Fisher information metric and thermodynamic length to characterize how sensitively the folded-state probability responds to changes in environmental conditions. As an illustrative application, we analyze the folding of the small protein 1YZM using a contact-based estimate of the internal entropy loss and a first-order model of crowding and osmolyte effects. We derive an effective entropy loss that is consistent in magnitude with previous estimates for small single-domain proteins and compute the Fisher metric element associated with crowding. While the numerical results are intentionally modest and phenomenological, the framework is fully reproducible and designed to be extended to more detailed models and additional environmental variables. We discuss limitations and future directions, including the incorporation of more realistic free-energy surfaces and Markov state models, with the long-term goal of quantifying the robustness of protein folding under cellular control of environmental entropy.