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

• Main Authors: Mendes, Hammurabi, Istrail, Sorin
• Format: Journal Article
• Language: English
• Published: 02-04-2014
• Subjects: Computer Science - Computational Engineering, Finance, and Science; Computer Science - Computer Science and Game Theory
• DOI: 10.48550/arxiv.1404.0672

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.