Principles for Optimal Cooperativity in Allosteric Materials.

Yan L; Ravasio R; Brito C; Wyart M

doi:10.1016/j.bpj.2018.05.015

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Journal article

Principles for Optimal Cooperativity in Allosteric Materials.

Yan L Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California.
Ravasio R Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
Brito C Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil.
Wyart M Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. Electronic address: matthieu.wyart@epfl.ch.

2018-06-21

Published in:

Biophysical journal. - 2018

English Allosteric proteins transmit a mechanical signal induced by binding a ligand. However, understanding the nature of the information transmitted and the architectures optimizing such transmission remains a challenge. Here we show, using an in silico evolution scheme and theoretical arguments, that architectures optimized to be cooperative, which efficiently propagate energy, qualitatively differ from previously investigated materials optimized to propagate strain. Although we observe a large diversity of functioning cooperative architectures (including shear, hinge, and twist designs), they all obey the same principle of displaying a mechanism, i.e., an extended soft mode. We show that its optimal frequency decreases with the spatial extension L of the system as L-d/2, where d is the spatial dimension. For these optimal designs, cooperativity decays logarithmically with L for d = 2 and does not decay for d = 3. Overall, our approach leads to a natural explanation for several observations in allosteric proteins and indicates an experimental path to test if allosteric proteins lie close to optimality.

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