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Thermodynamic Hypothesis as Social Choice: An Impossibility Theorem for Protein Folding

Protein Folding is concerned with the reasons and mechanism behind a protein's tertiary structure. The thermodynamic hypothesis of Anfinsen postulates an universal energy function (UEF) characterizing the tertiary structure, defined consistently across proteins, in terms of their aminoacid sequence. We consider the approach of examining multiple protein structure descriptors in the PDB (Protein Data Bank), and infer individual preferences, biases favoring particular classes of aminoacid interactions in each of them, later aggregating these individual preferences into a global preference. This 2-step process would ideally expose intrinsic biases on classes of aminoacid interactions in the UEF itself. The intuition is that any intrinsic biases in the UEF are expressed within each protein in a specific manner consistent with its specific aminoacid sequence, size, and fold (consistently with Anfinsen's thermodynamic hypothesis), making a 1-step, holistic aggregation less desirable. Our intention is to illustrate how some impossibility results from voting theory would apply in this setting, being possibly applicable to other protein folding problems as well. We consider concepts and results from voting theory and unveil methodological difficulties for the approach mentioned above. With our observations, we intend to highlight how key theoretical barriers, already exposed by economists, can be relevant for the development of new methods, new algorithms, for problems related to protein folding.