Force and Scale Dependence of the Elasticity of Self-Assembled DNA Bottle Brushes

Márcio Santos Rocha, Ingeborg M. Storm, Raniella Falchetto Bazoni, Ésio Bessa Ramos, Armando Hernandez-Garcia, Martien A. Cohen Stuart, Frans Leermakers , and Renko de Vries

As a model system to study the elasticity of bottle-brush polymers, we here introduce self-assembled DNA bottle brushes, consisting of a DNA main chain that can be very long and still of precisely defined length, and precisely monodisperse polypeptide side chains that are physically bound to the DNA main chains. Polypeptide side chains have a diblock architecture, where one block is a small archaeal nucleoid protein Sso7d that strongly binds to DNA. The other block is a net neutral, hydrophilic random coil polypeptide with a length of exactly 798 amino acids. Light scattering shows that for saturated brushes the grafting density is one side chain per 5.6 nm of DNA main chain. According to small-angle X-ray scattering, the brush diameter is D = 17 nm. By analyzing configurations of adsorbed DNA bottle brushes using AFM, we find that the effective persistence of the saturated DNA bottle brushes is Peff = 95 nm, but from force–extension curves of single DNA bottle brushes measured using optical tweezers we find Peff = 15 nm. The latter is equal to the value expected for DNA coated by the Sso7d binding block alone. The apparent discrepancy between the two measurements is rationalized in terms of the scale dependence of the bottle-brush elasticity using theory previously developed to analyze the scale-dependent electrostatic stiffening of DNA at low ionic strengths.

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Onset of Non-Continuum Effects in Microrheology of Entangled Polymer Solutions

Cole D. Chapman, Kent Lee, Dean Henze, Douglas E. Smith, and Rae M. Robertson-Anderson

Microrheology has emerged as a powerful approach for elucidating mechanical properties of soft materials and complex fluids, especially biomaterials. In this technique, embedded microspheres are used to determine viscoelastic properties via generalized Stokes–Einstein relations, which assume the material behaves as a homogeneous continuum on the length scale of the probe. However, this condition can be violated if macromolecular systems form characteristic length scales that are larger than the probe size. Here we report observations of the onset of this effect in DNA solutions. We use microspheres driven with optical tweezers to determine the frequency dependence of the linear elastic and viscous moduli and their dependence on probe radius and DNA length. For well-entangled DNA, we find that the threshold probe radius yielding continuum behavior is 3× the reptation tube diameter, consistent with recent theoretical predictions. Notably, this threshold is significantly larger than the mesh size of the polymer network, and larger than typical probe sizes used in microrheology studies.

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Force–Fluctuation Relation of a Single DNA Molecule

Takeshi Baba, Takahiro Sakaue, and Yoshihiro Murayama

We observed transverse fluctuations of single DNA molecules by fluorescence microscopy. The end-to-end distance of DNA molecules was varied by using dual trap optical tweezers, and the force–fluctuation relation was experimentally obtained in wide ranges of the force regime. In strong force regime, the theory of a stretched worm-like chain with fixed both ends explains the experimental results. On the other hand, in the low force regime, the fluctuations approach the value for an ideal ring polymer. We introduce an interpolate formula for the force–fluctuation relation by considering strong and low force limits, which captures the overall trend of experimental results. The proposed force–fluctuation relation will be useful for quantitative discussions in various sectors of polymer physics and biological processes which involve the conformation change of DNA and other biopolymers, where the loading and the fluctuation are relevant factors.

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Poly(ethylene oxide) Adsorption onto and Desorption from Silica Microspheres: New Insights from Optical Tweezers Electrophoresis

Jan A. van Heiningen and Reghan J. Hill

By measuring the changing electrophoretic mobility of single optically trapped silica microspheres (radius a ≈ 0.4 μm) during poly(ethylene oxide) homopolymer adsorption and desorption, we study polymer-layer kinetics at various polymer solution flow rates, concentrations, molecular weights, and polydispersities. At polymer concentrations c 5 ppm (mg L–1), Péclet numbers Pe 20, and Reynolds numbers Re 1, the adsorbing layer growth is mass-transport-limited, with time scales 10 s that are resolved on the uniquely small, micrometer length scale of optical tweezers electrophoresis (OTE) experiments. However, during adsorption, layer growth becomes limited by surface diffusion, reconformation, and exchange processes. Two characteristic relaxation times are revealed by the OTE time series. The faster time scale increases with polymer concentration and plateaus to 3 s when c 10 ppm. This reflects layer development kinetics limited by surface diffusion and reconformation. The slower time scale is 100 s and reflects polymer exchange, which thermodynamically favors large adsorbed coils when solutions are polydisperse. Desorption is even slower but occurs faster than expected by local-equilibrium theory, possibly because of high shear rates 100 s–1. The dynamic states probed by OTE are often sufficiently far from equilibrium that they cannot be adequately described by theories for equilibrium polymer adsorption, mass-transport-limited kinetics, or kinetics based on local equilibrium.

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Anisotropic hydrodynamic mean-field theory for semiflexible polymers under tension

Hinczewski, M., Netz, R.R.

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and it treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters.

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Forces of Interaction between Poly(2-vinylpyridine) Brushes As Measured by Optical Tweezers

Mahdy M. Elmahdy, Alla Synytska, Astrid Drechsler, Christof Gutsche, Petra Uhlmann, Manfred Stamm and Friedrich Kremer

Forces of interaction within single pairs of poly(2-vinylpyridine) (P2VP) grafted colloids have been measured by optical tweezers (OT) with an extraordinary resolution of ±0.5 pN. Parameters to be varied are the concentration and type of salt (KCl, CaCl₂, and LaCl₃) of the surrounding medium as well as its pH. The observed force−distance relation is quantitativelydescribed by the Jusufi model [Colloid Polym. Sci. 2004, 282, 910−917] for spherical polyelectrolyte brushes which takes into account the entropic effect of the counterions and enables one to estimate the ionic concentration inside the brush. The transition from an osmotic to the salted brush regime is analyzed in detail. For the scaling of the brush height a power law is found having an exponent of 0.24 ± 0.01, which ranges between the values expected for spherical and planar brushes. At pH 4 a strong transition from a brush to a pancake conformation takes place.

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