A (possible) mathematical model to describe biological "context-dependence" : case study with protein structure

TL;DR

This paper proposes a formal mathematical model to describe biological context-dependence, using a hierarchical 'Context tree' structure, and applies it to analyze factors influencing protein structure.

Contribution

It introduces a novel hierarchical 'Context tree' model to rigorously represent biological context-dependence and demonstrates its application to protein structure analysis.

Findings

Interactions between biological contexts are transitive but non-commutative.

Hierarchical dependence models biological properties effectively.

Algorithmic implementation of the 'Context tree' was achieved.

Abstract

Context-dependent nature of biological phenomena are well documented in every branch of biology. While there have been few previous attempts to (implicitly) model various facets of biological context-dependence, a formal and general mathematical construct to model the wide spectrum of context-dependence, eludes the students of biology. An objective and rigorous model, from both 'bottom-up' as well as 'top-down' perspective, is proposed here to serve as the template to describe the various kinds of context-dependence that we encounter in different branches of biology. Interactions between biological contexts was found to be transitive but non-commutative. It is found that a hierarchical nature of dependence amongst the biological contexts models the emergent biological properties efficiently. Reasons for these findings are provided with a general model to describe biological reality. Scheme to algorithmically implement the hierarchic structure of organization of biological contexts was achieved with a construct named 'Context tree'. A 'Context tree' based analysis of context interactions among biophysical factors influencing protein structure was performed.