  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.
