Criteria to observe mesoscopic emergence of protein biophysical properties

TL;DR

This paper introduces a mathematical model to determine when and how macroscopic biophysical properties of proteins emerge from complex atomic interactions, bridging nano-scale details and observable mesoscopic phenomena.

Contribution

It proposes a computational framework for assessing the emergence of protein properties from atomic interactions, including both linear and non-linear models.

Findings

Derived observability criteria for linear atomic interactions.

Extended criteria to non-linear atomic interactions.

Provides a basis for understanding mesoscopic emergence in proteins.

Abstract

Proteins are regularly described with some general indices (mass fractal dimension, surface fractal dimension, entropy, enthalpy, free energies, hydrophobicity, denaturation temperature etc..), which are inherently statistical in nature. These general indices emerge from innumerable (innately context-dependent and time-dependent) interactions between various atoms of a protein. Many a studies have been performed on the nature of these inter-atomic interactions and the change of profile of atomic fluctuations that they cause. However, we still do not know, under a given context, for a given duration of time, how does a macroscopic biophysical property emerge from the cumulative inter-atomic interactions. An exact answer to that question will involve bridging the gap between nano-scale distinguishable atomic description and macroscopic indistinguishable (statistical) measures, along the mesoscopic scale of observation. In this work we propose a computationally implementable mathematical model that derives expressions for observability of emergence of a macroscopic biophysical property from a set of interacting (fluctuating) atoms. Since most of the aforementioned interactions are non-linear in nature; observability criteria are derived for both linear and the non-linear descriptions of protein interior. The study assumes paramount importance in 21st-century biology, from both the theoretical and practical utilitarian point of view.