Mesoscopic model for mechanical characterization of biological protein materials

Gwonchan Yoon1, Hyeong-Jin Park1, Sungsoo Na1,*, and Kilho Eom2,† 1Department of Mechanical Engineering, Korea University, Seoul 136-701, Republic of Korea 2Nano-Bio Research Center, Korea Institute of Science & Technology (KIST), Seoul 136-791, Republic of Korea

• Corresponding Author. E-mail: nass@korea.ac.kr
  † Corresponding Author. E-mail: eomkh@kist.re.kr

1 Abstract Mechanical characterization of protein molecules has played a role on gaining insight into the biological functions of proteins, since some proteins perform the mechanical function. Here, we present the mesoscopic model of biological protein materials composed of protein crystals prescribed by Go potential for characterization of elastic behavior of protein materials. Specifically, we consider the representative volume element (RVE) containing the protein crystals represented by Cα atoms, prescribed by Go potential, with application of constant normal strain to RVE. The stress-strain relationship computed from virial stress theory provides the nonlinear elastic behavior of protein materials and their mechanical properties such as Young’s modulus, quantitatively and/or qualitatively comparable to mechanical properties of biological protein materials obtained from experiments and/or atomistic simulations. Further, we discuss the role of native topology on the mechanical properties of protein crystals. It is shown that parallel strands (hydrogen bonds in parallel) enhance the mechanical resilience of protein materials.

Keywords: Mechanical Property; Protein Crystal; Go Model; Virial Stress; Young’s Modulus

2 INTRODUCTION Several proteins bear the remarkable mechanical properties such as super-elasticity, high yield-strength, and high fracture toughness.1-5 Such remarkable properties of some proteins have attributed to the mechanical functions. For instance, spider silk proteins exhibit the super-elasticity relevant to spider-silk’s function.4,5 Specifically, the super- elasticity of spider silk plays a role on the ability of spider silk to capture a prey such that high extensibility enables the spider silk to convert the kinetic energy of flying prey into the heat dissipation, resulting in the capability of capturing the prey. Furthermore, it has recently been found that spider silk protein possesses the remarkable mechanical properties such as yield strength comparable to that of high-tensile steel and fracture toughness better than that of Kevlar.6 This highlights that understanding of mechanical behavior of protein materials such as spider silk may provide the key concept for design of biomimetic materials, and that mechanical characterization of protein materials may allow for gaining insight into the biological functions of mechanical proteins.

Mechanical characterization of biological molecules such as proteins has been successfully implemented by using atomic force microscopy (AFM), optical tweezers, or fluorescence method. AFM has been broadly employed for characterization of mechanical bending motion of nanostructures such as suspended nanowires,7-9 and biological fibers such as microtubules.10 Fluorescence method for a cantilevered fibers such as microtubules11 and/or DNA molecules12 has allowed one to understand the relationship between persistent length (related to bending rigidity) and contour length, enabling the validation of the continuum model of biomolecules such as microtubule and DNA. In last decade, since the pioneering works by Bustamante and coworkers13,14 and Gaub and coworkers,15,16 optical tweezer and/or AFM has enabled them to

3 characterize the microscopic mechanical behavior of proteins such as protein unfolding mechanics. Such protein unfolding experiments has been illuminated in that these studies may provide the free energy landscape of proteins related to protein folding mechanism.17,18 Nevertheless, microscopic characterization such as protein unfolding mechanics may not be sufficient to understand the remarkable mechanical properties of biological materials.

Computational simulation for mechanical characterization of proteins has been taken into account based on atomistic model such as molecular dynamics19 and/or coarse-grained model.20 Atomistic model such as steered molecular dynamics (SMD) simulation has allowed one to gain insight into protein unfolding mechanics.19,21 However, such SMD simulation has been still computationally limited to small proteins since the time scale available for SMD is not relevant to the time scale for AFM experiments of protein unfolding mechanics. Recently, the coarse-grained model such as Go model has been recently revisited for mimicking the protein unfolding experiments.20,22 It is remarkable that such revisited Go model has provided

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