Force generation by a propagating wave of supramolecular nanofibers

Out-of-equilibrium events create diverse spatiotemporal patterns in living cells, playing essential roles in functions like cell division and migration. These patterns generate force, as seen in the actin waves driving cell membrane extension during migration. Mimicking these dynamic patterns in artificial systems offers the potential to create soft materials with life-like characteristics like autonomy and adaptability. While previous research explored stimulus-responsive supramolecular nanofibers, achieving spatiotemporal control over their formation and degradation, coupled with precise force measurement, remained a challenge. This study aims to address these challenges by designing a system that generates a propagating wave of supramolecular nanofibers and quantitatively measuring the force generated by this wave. The inspiration comes from the dynamics of actin filaments in lamellipodia, where specific proteins regulate polymerization and depolymerization. The research seeks to bridge the gap between biological and artificial systems, paving the way for advanced soft materials with cell-mimetic functions.

The study draws upon existing literature on out-of-equilibrium biochemical reactions and their ability to generate spatial-temporal patterns such as oscillations and waves. The authors cite examples in biology, including Min systems for cell division and actin waves for cell migration, highlighting the force-generating capacity of these patterns. They review previous work on out-of-equilibrium dynamic patterns in supramolecular architectures, noting efforts to create self-oscillating gels, self-walking actuators, and autonomous mass transport using polymer-based soft materials. Previous attempts to generate spatiotemporal patterns using stimulus-responsive supramolecular nanofibers are also discussed, highlighting limitations in achieving spatiotemporal coupling of formation and degradation. The lack of precise force measurements in artificial spatiotemporal patterns is also emphasized. This research is positioned as a significant step towards achieving spatiotemporal control and quantitative force measurement in artificial supramolecular systems.

The researchers designed a chemical reaction network inspired by actin dynamics to control the formation and degradation of supramolecular nanofibers. They utilized a peptide-type hydrogelator, BPmoc-F3, containing two functional groups: carboxylate and boronobenzyl. Zinc ions (Zn2+) were used as a formation stimulus, inducing nanofiber formation through coordination with the carboxylate group. Hydrogen peroxide (H2O2), generated enzymatically from glucose oxidase (GOx) and glucose, acted as the degradation stimulus, decomposing the nanofibers via a 1,6-elimination reaction on the boronobenzyl group. The orthogonality of these stimuli ensures precise control. The researchers employed a tube inversion method to assess Zn2+-triggered hydrogelation, and real-time confocal laser scanning microscopic (CLSM) imaging to visualize the formation and degradation processes. The CLSM imaging was conducted using a fluorescent probe (BP-TMR) to track nanofiber dynamics. To generate the propagating wave, a droplet containing BPmoc-F3, BP-TMR, and GOx was sandwiched between glass plates, and a mixture of Zn2+ and glucose was added at the droplet's edge. The propagating wave was analyzed through time-lapse CLSM imaging, quantifying the wave velocity and propagation distance. A reaction-diffusion model was developed to simulate the propagating wave, considering nanofiber formation (Zn2+-promoted and independent processes) and degradation. The simulation helped elucidate the factors contributing to wave emergence, including concentration gradients of stimuli and the nanofiber's diffusion coefficient. Finally, to measure force generation, PEG-coated fluorescent beads were incorporated into the system. Bead displacement during wave propagation was monitored via real-time CLSM imaging, and the force was calculated using Stokes' law, considering the viscosity of the medium. A control experiment with homogeneous nanofiber formation and degradation was also conducted. The persistence length of the nanofibers was determined using image analysis of CLSM images.

The study successfully demonstrated the generation of a propagating wave of supramolecular nanofibers using two orthogonal chemical stimuli: Zn2+ for formation and H2O2 (generated from GOx and glucose) for degradation. Real-time CLSM imaging showed the spatiotemporally coupled formation and collapse of nanofibers across a millimeter scale. The wave propagation was quantitatively characterized, with an average velocity of approximately 54 ± 8 µm/min. Numerical simulation based on a reaction-diffusion model confirmed the experimental observations and revealed the importance of concentration gradients of both formation and degradation stimuli, and the relatively low diffusion coefficient of the nanofibers, in driving the wave propagation. The simulation accurately reproduced the propagating wave behavior, highlighting the critical role of the concentration gradient of the degradation stimulus in maintaining wave propagation. Importantly, the study successfully quantified the force generated by the propagating wave, estimating it to be approximately 0.005 pN. This force was sufficient to move 500 nm diameter nanobeads along the wave direction, a phenomenon not observed in control experiments with homogeneous nanofiber formation/degradation. The measured force was attributed to chemophoresis and/or depletion forces arising from the concentration gradients. Analysis of the CLSM images also allowed for the determination of the persistence length of the nanofibers.

The successful generation and characterization of a propagating wave of supramolecular nanofibers demonstrates a novel approach to creating dynamic, force-generating artificial systems. The results highlight the power of rationally designed reaction networks, inspired by biological systems, to achieve complex spatiotemporal control over supramolecular assemblies. The findings have implications for the development of active soft materials with cell-like functions, such as motility and self-organization. The quantitative measurement of force generated by the wave opens avenues for studying the interplay between chemical reactions and mechanical forces in artificial systems. The model developed provides valuable insights into the underlying mechanisms governing the wave propagation, guiding future design of such systems. The observation of bead movement showcases the potential for creating micro-machines and micro-robots powered by chemical reactions.

This research successfully demonstrated the generation of a force-generating propagating wave of supramolecular nanofibers. The study highlights the potential of bio-inspired reaction networks in creating artificial systems exhibiting complex spatiotemporal behavior and mechanical function. Future research could explore optimizing the system for greater force generation, exploring different hydrogelators and stimuli, and investigating the potential applications of these systems in areas such as micro-robotics and drug delivery.

The study focused on a specific peptide hydrogelator and chemical stimuli. The generalizability of the findings to other systems requires further investigation. The force measurement relies on simplified assumptions about viscosity and fluid dynamics. More sophisticated techniques could be employed to improve the accuracy of force determination. The numerical model is a simplification of the complex processes occurring in the system. While the model effectively reproduced the wave propagation, other factors might also play a role. The manual injection of the stimuli introduces some variability in the experimental results, though the reproducibility was confirmed.