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Increasing valence pushes DNA nanostar networks to the isostatic point

Nathaniel Conrad,T. Kennedy,D. Fygenson,O. Saleh

Published 2019 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance Maxwell (1864) predicted that 3D networks of beams fixed to junctions through freely rotating joints will be rigid only if at least six beams emanate from each junction. This concept is key to macroscopic design of trussed structures, but its relevance to microscopic networks, where thermal fluctuations are large, such as in biomolecular gels, is not as clear. Here, we exploit DNA nanotechnology to create gels of defined connectivity and demonstrate that gel mechanics are controlled by an interplay between entropic effects, network structure, and Maxwell’s rigidity criterion. The classic picture of soft material mechanics is that of rubber elasticity, in which material modulus is related to the entropic elasticity of flexible polymeric linkers. The rubber model, however, largely ignores the role of valence (i.e., the number of network chains emanating from a junction). Recent work predicts that valence, and particularly the Maxwell isostatic point, plays a key role in determining the mechanics of semiflexible polymer networks. Here, we report a series of experiments confirming the prominent role of valence in determining the mechanics of a model system. The system is based on DNA nanostars (DNAns): multiarmed, self-assembled nanostructures that form thermoreversible equilibrium gels through base pair-controlled cross-linking. We measure the linear and nonlinear elastic properties of these gels as a function of DNAns arm number, f, and concentration [DNAns]. We find that, as f increases from three to six, the gel’s high-frequency plateau modulus strongly increases, and its dependence on [DNAns] transitions from nonlinear to linear. Additionally, higher-valence gels exhibit less strain hardening, indicating that they have less configurational freedom. Minimal strain hardening and linear dependence of shear modulus on concentration at high f are consistent with predictions for isostatic systems. Evident strain hardening and nonlinear concentration dependence of shear modulus suggest that the low-f networks are subisostatic and have a transient, potentially fractal percolated structure. Overall, our observations indicate that network elasticity is sensitive both to entropic elasticity of network chains and to junction valence, with an apparent isostatic point 5

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