TITLE:
Global Geometrical Constraints on the Shape of Proteins and Their Influence on Allosteric Regulation
AUTHORS:
Naoto Morikawa
KEYWORDS:
Differential Geometry, Protein Structure, Discrete Mathematics, Allosteric Regulation, Simultaneous Equations for Shape
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.10,
October
24,
2018
ABSTRACT: Proteins are the workhorse molecules of the cell, which are obtained by folding
long chains of amino acids. Since not all shapes are obtained as a folded
chain of amino acids, there should be global geometrical constraints on the
shape. Moreover, since the function of a protein is largely determined by its
shape, constraints on the shape should have some influence on its interaction
with other proteins. In this paper, we consider global geometrical constraints
on the shape of proteins. Using a mathematical toy model, in which proteins
are represented as closed chains of tetrahedrons, we have identified not only
global geometrical constraints on the shape of proteins, but also their influence
on protein interactions. As an example, we show that a garlic-bulb like
structure appears as a result of the constraints. Regarding the influence of
global geometrical constraints on interactions, we consider their influence on
the structural coupling of two distal sites in allosteric regulation. We then
show the inseparable relationship between global geometrical constraints and
protein interactions; i.e. they are different sides of the same coin. This finding
could be important for the understanding of the basic mechanisms of allosteric
regulation of protein functions.