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Global Geometrical Constraints on the Shape of Proteins and Their Influence on Allosteric Regulation

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Document pages: 40 pages

Abstract: Proteins are the workhorse molecules of the cell, which are obtained by foldinglong chains of amino acids. Since not all shapes are obtained as a foldedchain of amino acids, there should be global geometrical constraints on theshape. Moreover, since the function of a protein is largely determined by itsshape, constraints on the shape should have some influence on its interactionwith other proteins. In this paper, we consider global geometrical constraintson the shape of proteins. Using a mathematical toy model, in which proteinsare represented as closed chains of tetrahedrons, we have identified not onlyglobal geometrical constraints on the shape of proteins, but also their influenceon protein interactions. As an example, we show that a garlic-bulb likestructure appears as a result of the constraints. Regarding the influence ofglobal geometrical constraints on interactions, we consider their influence onthe structural coupling of two distal sites in allosteric regulation. We thenshow the inseparable relationship between global geometrical constraints andprotein interactions; i.e. they are different sides of the same coin. This findingcould be important for the understanding of the basic mechanisms of allostericregulation of protein functions.

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