A molecular modeling study of the supersecondary structure nanomechanics

Minin K.A., Zhmurov A.A., Zhmurova N.V.1

Moscow Institute of Physics and Technology

1Ryazan State University named for S. Yesenin

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One of the most common supersecondary structure are coiled coils, that consist of several $\alpha$-helices, wrapped around one another. In many cases, coiled coils can be related to machanical function of the protein. For example, the myosin tail is a two stranded coiled coil. When muscle contracts, the energy of the motion of the head of the molecule is passed along this coiled coils. Another example is a fibrinogen molecule --- the main protein of the blood clot. Fibrinogen has a trinodular structure with three globular parts connected by two three-stranded coiled coils. Cell cytoskeleton contains intermediate filaments --- another example of the superhelical proteins.

Mechanical properties of the coiled coils has become a frequent target for experimental and computational research. These studies revealed unique mechanical properties of these systems. When the external tension is low, their mechanical response is elastic. After certain threshold extension is reached, the system switches into regime of plastic deformation. When the system is fully extended, the force grows non-linearly. Today this unique mechanical footprint of the coiled coils is related to the phase transition from $\alpha$-helices to $\beta$-sheet.

In this work, we used molecular modeling to study several superhelical structures. We selected molecular systems that have different structural features, contain different number of $\alpha$-helices, have parallel and anti-parallel structures. All the system show similar force-extension profiles. The existence of the critical force at which the systems switch from elastic to the plastic behavior was connected to the $\alpha$-to-$\beta$ transition. We show that for parallel coiled coils the critical force linearly depends on the number of helices with tangent greater than one. This shows that there is a cooperativity between $\alpha$-helices in the coiled coils. Interestingly, the critical force for anti-parallel coiled coils is lower when compared to parallel coiled coils, but the spring constant in the elastic regime is higher.

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