Deformation-Dependent Nonlinear Relaxation in Dense DNA Solutions Akinori Miyamoto and Yoshihiro Murayama + Department of Applied Physics, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan (Received January 13, 2022; accepted May 23, 2022; published online June 16, 2022) We investigated the relaxation process after deformation induced by an optically trapped bead to elucidate the effect of microstructural deformation on the viscoelasticity of a dense DNA solution. The relaxation changed from a double exponential to a power law with an exponent of -0.5, as the degree of deformation increased. Using a simple phenomenological model, the viscoelastic parameters were determined from the experimental data of deformation- dependent nonlinear relaxation. The evaluated elasticity and viscosity confirmed that this model is reasonable for describing the viscoelasticity of dense DNA solutions. Microrheology 1,2) has attracted considerable interest in the recent quarter century in physics, 3) biology, 4–6) and medi- cine. 7) Optical tweezers, 7,8) fluorescent probes, 9) and atomic force microscopy 4,5,10,11) have been widely used to measure the viscoelasticity of a cell on the micron scale. These viscoelastic responses are highly complex and exhibit a nonlinear response, 12) power-law (P-L) decay, 4,10,12) and anomalous diffusion. 9,13) These findings have motivated extensive efforts to understand the viscoelastic properties induced by microstructures consisting of biopolymers in vitro. 14–16) In particular, deoxyribonucleic acid (DNA) solutions are useful for investigating the dependence of polymer length, 17) conformation (linear or circular), 18) and the degree of entanglement 18,19) on the mechanical properties because they can be easily controlled using molecular biology techniques. Viscoelasticity also depends on the probe size 20) and shear rate. 21) A DNA solution is relatively simple compared to the inside of a cell, and reptation theory is partially applicable to the description of an entangled DNA solution. 20,22) However, there is no unified view to explain the viscoelasticity of DNA solutions at the microscale. One reason is that the degree of deformation of a microstructure, such as the mesh structure, depends on the observation method. For passive microrheology, the size of the deformation of the microstructure is typically less than one micron from observing the Brownian motion of a probe particle 1,2,17) or active microrheology using the sinusoidal oscillation of a probe particle. 20) However, when the moving distance of a probe particle exceeds a few microns, the deformation size increases. As there is no crosslinking between DNA molecules, the microstructure deformation can be highly sensitive to external stress. 17) The large deforma- tion leads to an inhomogeneous concentration at the micro- scale; therefore, the viscoelasticity differs from that observed using a conventional rheometer. 23–25) This study focuses on the relationship between the microstructure’s deformation degree and the viscoelasticity of the DNA solution. We can easily confirm the elasticity of the DNA solution as follows: we trap a micron-sized bead using optical tweezers, move it a certain distance, and then release it from the trap. For a simple viscous fluid, such as water, the bead exhibits Brownian motion after release. In contrast, for a dense DNA solution, the bead moves backward after being released because of the mesh or entanglement elasticity and reaches an equilibrium. 21) This backward motion after being released is the relaxation process. For simple viscoelastic fluids, which can be described by a single Maxwell or Jeffreys model, 24) the relaxation obeys an exponential law, and the relaxation time is determined by viscosity and elasticity. However, for dense DNA solutions, single exponential relaxation for small deformations (0.2 μm) by the sinusoidal oscillation of a probe particle and double exponential (D-E) relaxation for large deformations (16 μm) have been observed. 24) Furthermore, in a dense microtubule solution, the relaxation of stress changes from D-E to P-L with an exponent of -0.5. 26) These nonlinear relaxations can be related to the dynamics of the microstructure’s deformation around the probe particle; however, the complex relaxation process has not been explained. In this study, we performed move-and-release experiments using optical tweezers in a dense DNA solution to elucidate the effects of the degree of deformation on the relaxation process. We changed the moving distance to change the degree of deformation, and the relationship between the moving distance and relaxation process was investigated. As the moving distance increased, we observed that the relaxation changed from D-E to P-L with an exponent of -0.5. Using a simple phenomenological model, we deter- mined the viscoelastic parameters from the experimental data of deformation-dependent nonlinear relaxation. Interestingly, a similar nonlinear relaxation appears in the theoretical model that considers fluctuating viscosity. 27) We used 0.6 mg mL -1 Klenow-fragment-treated λ-phage DNA of 48.5 kbp (16.5 μm in contour length and 0.5 μm in gyration radius) in 10 mM Tris–HCl and 1 mM ethyl- enediaminetetraacetic acid (EDTA) at pH 8:0  0:1. The DNA solution was placed in a handmade chamber consisting of a silicone spacer (thickness 0.13 mm) sandwiched between two coverslips. The optical tweezers consisted of an Nd- YAG laser with a wavelength of 1064 nm and an objective lens (100 oil immersion objective, 1.4 NA, Olympus), and the stiffness of the optical trap was 14.7 pN μm -1 . We trapped a polystyrene bead (diameter d ¼ 3:0 μm, Polysciences) and moved it at a constant speed by changing the focal position of the optical trap parallel to the bottom surface. After moving the bead by a certain distance x m , it was released from the trap by closing the shutter in front of the laser. x m was varied by changing the closing time of the shutter, which was controlled using LabVIEW software (National Instruments). The beads were trapped 10 μm from the bottom surface to avoid the wall effect. All experiments were performed at 25:0  0:5 °C. The bead images were captured using a Journal of the Physical Society of Japan 91, 073801 (2022) https://doi.org/10.7566/JPSJ.91.073801 Letters 073801-1 © 2022 The Physical Society of Japan J. Phys. Soc. Jpn. 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