Elastic instability-mediated actuation by a supra-molecular polymer

In nature, fast, high-power-density actuation can be achieved through the release of stored elastic energy by exploiting mechanical instabilities in systems including the closure of the Venus flytrap and the dispersal of plant or fungal spores. Here, we use droplet microfluidics to tailor the geometry of a nanoscale self-assembling supra-molecular polymer to create a mechanical instability. We show that this strategy allows the build-up of elastic energy as a result of peptide selfassembly, and its releasewithinmillisecondswhen the buckled geometry of the nanotube confined within microdroplets becomes unstable with respect to the straight form. These results overcome the inherent limitations of self-assembly for generating large-scale actuation on the sub-second timescale and illuminate the possibilities and performance limits of irreversible actuation by supra-molecular polymers. Self-assembly is a ubiquitous phenomenon in nature that underlies the formation of the nanoscale machinery of life, including protein filaments, molecularmotors and other complex architectures. This process involves the molecular recognition and association of building blocks mediated by non-covalent interactions, ultimately leading to supra-molecular species with unique characteristics, such as the ability to assemble reversibly, to modulate structure stiffness and to respond to external stimuli. In biological systems, it has long been revealed that cellular movement and traction at surfaces is controlled by the self-assembly of cytoskeletal proteins. The self-assembly of biomimetic building blocks is also an attractive route towards force generation in an artificial setting due to the fact that such processes take place under ambient conditions, with no, or minimal, requirements for external energy input. However, due to the highly dynamical nature of molecular-level self-assembly phenomena, it has been challenging to achieve rapid movement on length scales exceeding that of the building blocks themselves. A strategy to overcome these limitations is to decouple the slow build-up of potential energy, typically in the form of elastic energy, from its rapid release by exploiting mechanical instabilities. Natural systems use mechanical instabilities to generate remarkably rapid movements, including the closure of the Venus flytrap or the dispersal of spores and seeds by plants, fungi or bacteria, but its coupling to self-assembly has not been reported. Here we focus on the dynamics of a dipeptide system, namely the self-assembly of diphenylalanine (FF) into nanostructures. By confining the growing nanostructures inside microdroplets and presenting real-time imaging, we show that the self-assembly process can result in the build-up of elastic energy from the buckling and bending of the nanostructures. To probe the force generated by the growth of self-assembled FF tubes, we used a microdroplet platform. FF was initially solubilized in acetic acid to form a stock solution of 100–300mgml that was flowed directly into the microfluidic device; in a first junction on the device, this stock solution was diluted in equal part with water, yielding a super-saturated solution of 50–150mgml FF. Immediately aftermixing, this solutionwas compartmentalized into microdroplets at the secondT-junction on-chip into a fluorinated oil phase. Droplets were subsequently collected and stored off-chip. We first observed the ability of FF building blocks (solution concentration 50mgml FF) to self-assemble into robust tubes as a result of the partial evaporation of the aqueous/acetic acid phase when droplets were kept on a glass coverslide. An array of evaporating droplets in close proximity to each other wasmonitored over time, and we were able to detect that the formation of tubes in one droplet was accompanied by their expansion into other droplets in the vicinity of aggregated droplets (Fig. 1a). On closer inspection, nanotube formation inside droplets was observed to initiate from a single nucleation site from which tubes emerged and subsequently grew through secondary nucleation until they reached the droplet boundaries. Over time, the tubes were seen to penetrate through the membrane formed by the double interface and grow further inside neighbouring droplets (Fig. 1b). We can quantify the forces implicated in FF self-assembly using classical nucleation theory. For a membrane formed by a thin oil layer between two aqueous droplets, exhibiting a surface tension σ , classical nucleation theory describes the free energy associated with the formation of a circular hole of radius r as a balance between the cost of the formation of the hole and the gain in surface energy: F(r)= 2πrγ − 2πr σ , where γ is the line tension (Fig. 1c). The competition between these two energy contributions leads to a free energy function F(r) having a maximum as a function of hole radius (Fig. 1c). The critical radius and energy barrier emerge from this argument as: r= γ /(2σ) and F= πγ /(2σ). For our experimental values of σ = 20 pNnm, γ = 2 pN, we find F=3.1×10 pNnm (see Supplementary Information for details). Linear FF assembly is thus able to generate forces that are sufficient to rupture water-in-oil double layer interfaces, but the rate of energy release is limited by the rate of FF self-assembly and