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.
Highlights
In this paper, we consider global geometrical constraints on the shape of proteins, using the mathematical toy model of proteins proposed in [1]
Proteins are the workhorse molecules of the cell, which are obtained by folding long chains of amino acids
Using a mathematical toy model, in which proteins are represented as closed chains of tetrahedrons, we have identified global geometrical constraints on the shape of proteins, and their influence on protein interactions
Summary
We consider global geometrical constraints on the shape of proteins, using the mathematical toy model of proteins proposed in [1]. The determination of protein structures which satisfy a set of constraints on inter-atomic distances, known as the distance geometry problem, is an important problem in structural biology [5]. In virology, another type of geometrical constraints, the symmetry of the virus structure, is considered. Protein molecules are obtained by folding a chain of linked parts and it is impossible to describe the shape of proteins by symmetry alone nor to describe their surface by tiling of basic subunits. The geometrical constraints on the shape of a molecule correspond to the constraints on the interaction between three molecules, such as allosteric regulations. Genocript (http://www.genocript.com) is the one-man bio-venture started by Naoto Morikawa in 2000 which is developing software tools for protein structure analysis
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