Journal of Mathematical Chemistry

, Volume 49, Issue 3, pp 643–665 | Cite as

Mathematical criteria to observe mesoscopic emergence of protein biochemical properties

Original Paper

Abstract

Proteins are regularly described with some general indices (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 studies have been performed on the nature of these interatomic 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 property emerge from the cumulative interatomic interactions. An exact answer to that question requires bridging the gap between nano-scale distinguishable atomic description and macroscopic indistinguishable (statistical) measures with mesoscopic description. In this work we propose a mathematical framework that derives expressions to observe emergence of a macroscopic biophysical property from a set of interacting (fluctuating) atoms. Since most of the protein interior interactions are non-linear in nature; observability criteria are derived for both linear and the non-linear descriptions of protein interior. Care has been taken (with extensive literature survey) to ensure that every pertinent bio-physical and bio-chemical facet of protein interior is taken into account, without compromising with the mathematical rigor. Two theorems (concerning mathematical description of protein structure) are proposed here that helps the nascent field of mesoscopic protein studies. Categorical schemes to relate mathematical formulations to studies of pKa shift, residual dipolar coupling, origin of hydrophobicity, drug discovery etc.—are provided to ensure their easy applicability. While the present work helps the theoretical discourse by providing a framework to understand the origin of a macroscopic property; ability of it to predict a priory whether the dynamics in a certain set of atoms or the couplings between them, can at all produce a biological property of interest or not, will account for tremendous saving of resource and effort.

Keywords

Mesoscopic origin Biochemical properties Emergence Observability Predictive mathematical framework Non-linear differential equations 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Bioinformatics CentreUniversity of PunePuneIndia
  2. 2.School of Information TechnologyJawaharlal Nehru UniversityNew DelhiIndia

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