Autonomous chemo-mechanical oscillations in crosslinked filamentous actin gels

Abstract

Mechanical oscillations play fundamental roles in cellular processes such as motility, signalling, and structural regulation; however, the mechanisms by which artificial cytoskeletal networks can be engineered to reproduce such autonomous oscillatory behaviours remain poorly understood. In this study, we demonstrate that a chemically polyethylene glycol-crosslinked filamentous actin hydrogel exhibits autonomous, long-lasting, and synchronised mechanical oscillations during self-organised polymerisation. These oscillations arise from chemo-mechanical responses coupled with the treadmilling polymerisation–depolymerisation equilibrium of filamentous actin. We propose that the rigid and highly hierarchical structure of the chemically crosslinked network plays an important role in the emergence of such autonomous mechanical oscillations. Our results reveal how hierarchical crosslinking and chemo-mechanical coupling drive sustained oscillations in active polymer networks, providing new insight into the fundamental mechanisms underlying autonomous dynamics in soft materials.

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Introduction

Mechanical oscillations are ubiquitous in living systems, manifesting as collective mechanical actions, such as the heartbeat, cytoskeletal transport, and cellular flocking. They are inherent processes for motility, communication, regulation, signalling, and other vital cellular activities. These dynamic cellular phenomena often arise from self-organised, ordered structures maintained under non-equilibrium conditions, where non-linear behaviour emerges from the collective dynamics of interacting components at lower constituent levels.^1–3 Many local mechanically active units propagate through the system via spatial diffusion, appearing as synchronised waves, sometimes coupled with physical interactions or chemical reactions.^4–6 The interconversion of chemical and mechanical energy is called a “chemo-mechanical” or “mechano-chemical process”.⁷ The viscoelastic properties of the system through which these waves diffuse are important, because they govern reaction-diffusion transport and the emergence of dynamic patterns. Living organisms exhibit persistent non-linear dynamics because they are mainly composed of soft tissues, biological gels that sustain specific viscoelastic properties. Soft tissues are typical hydrogels in which physically entangled and chemically crosslinked proteins and polysaccharides form a network, resulting in increased viscoelastic properties arising from the dynamic motion and friction between water and the polymer network.

Because non-linear dynamics often emerge from newly organised, highly ordered structures, constructing hierarchical architectures with suitable viscoelastic properties is important for designing synthetic systems capable of oscillatory functions. This approach also offers a pathway toward elucidating the mechanisms underlying emergent phenomena. A major challenge lies in integrating hierarchical structures with an active oscillator. Based on these assumptions, we synthesised chemically crosslinked F-actin hydrogels by polymerising globular actin (G-actin).⁸ Actin is the most abundant cytoskeletal protein in eukaryotes and consists of 375 amino acids, with a molecular weight of 42 000. It spontaneously polymerises and self-organises into bundles in cells and plays a pivotal role in maintaining the integrity and motility of eukaryotic cells.⁹ Such cytoskeletal proteins can form highly dynamic networks that exhibit mechanical oscillations and sustain the motility of the cell;¹⁰ therefore, we hypothesised that the gelation of polymerised F-actin would exhibit mechanical behaviour arising from its highly hierarchical structure. Notably, water-swollen hydrogels behave as elastic solids at the macroscopic scale, maintaining a definite shape without fluidity but acting as highly viscous fluids at the molecular scale, showing no convection. This unique characteristic originates from their high degree of swelling, which provides polymer-network spaces for water penetration and contributes to their viscoelastic response. In recent years, the study of active matter has further highlighted how cytoskeletal gels and motor-driven systems can generate large-scale mechanical work through molecular-level energy consumption.^11,12

While we previously reported the existence of mechanical oscillations in F-actin gels in a monograph,¹³ the specific chemical basis of the network and the quantitative relationship between the hierarchical structure and oscillatory parameters remain to be fully elucidated. A deeper understanding of these factors is essential to establish such systems as independent and complete models for emergent phenomena. In this study, we demonstrate that chemically crosslinked F-actin hydrogels exhibit autonomous, long-lasting, and synchronized mechanical oscillations during self-organized polymerization. We provide a comprehensive qualitative analysis of these oscillations and discuss how the hierarchical architecture of the crosslinked network facilitates the accumulation and release of mechanical strain. Our results suggest that the oscillation emerges from a feedback loop between the treadmilling polymerization–depolymerization equilibrium and the cooperative structural response of the F-actin network. We therefore assume that the rigid and highly hierarchical structure of the chemically crosslinked network play an important role in the emergence of autonomous mechanical oscillations.

Results and discussion

We previously reported the formation of a chemically crosslinked F-actin gel via polymerisation of G-actin in the presence of a polyethylene glycol (PEG) actin dimer.⁸ The PEG actin dimer contains two G-actin molecules at both chain ends of the di-maleimide-terminated PEG and binds cysteine 374 of G-actin. In vitro, G-actin polymerizes to form F-actin upon increasing the ionic strength. In the presence of PEG-actin dimers, the individual G-actin subunits are incorporated into distinct F-actin filaments, resulting in the formation of a hydrogel in which the F-actin filaments are chemically crosslinked by PEG bridges.⁸ In contrast to conventional synthetic polymer gels, which typically consist of amorphous networks formed via irreversible covalent bonding, the F-actin network arises from the spontaneous self-assembly of G-actin into a highly hierarchical and ordered structure. A distinctive feature of this F-actin gel is its dynamic and reversible nature; the network can undergo polymerization and depolymerization in response to external stimuli, such as changes in ionic strength or the application of shear strain.⁸ Consequently, the system exhibits a reversible sol–gel transition, reflecting the inherent plasticity of the biological macromolecular assembly.⁸ Notably, this F-actin gel undergoes a cooperative breakdown when subjected to shear strain.⁸ This reflects the intrinsic nature of F-actin, which exhibits cooperative depolymerization into G-actin in response to torsional strain. In our hierarchical network, such molecular-level mechanics are likely amplified, allowing the macroscopic gel structure to respond to mechanical stimuli in a highly synchronized and collective manner.

Progress in G-actin polymerisation was monitored as a continuous and intensive increase in the storage modulus (G′) of the F-actin gel. Fig. 1 shows the initial growth process of G′ observed under different strains. The initial G′ of the G-actin solution before polymerisation was on the order of 10⁻³–10⁻² Pa, increasing rapidly to several kPa within 1 h. The final G′ value of the F-actin gel exceeded the loss modulus (G″) by more than two orders of magnitude over a wide range of frequencies (Fig. S1), confirming that the F-actin gel behaves as a chemically crosslinked elastic. A gel reportedly exhibits predominantly elastic behaviour when G′ > G″, indicating energy storage within the network.¹⁴

Fig. 1 A. Time profiles of relative G′ after PEG 3400-crosslinked G-actin polymerisation. G′ was measured at a shear strain of 0.5% (orange), 1.0% (red), and 2.0% (light blue), and a frequency of 1.0 Hz. B. The corresponding power spectra. The power spectra were calculated using the Microcal Origin 8 software.

Interestingly, G′ increases with intensive mechanical oscillation, as shown in Fig. 1. The oscillation was stable and continued for more than 8 h with a nearly constant frequency and amplitude throughout the polymerisation process and thereafter. The power spectrum of G′ for these actin gels showed that the oscillations resembled a reverse-sawtooth wave. For the characterization of the mechanical oscillations, four completely independent experiments were conducted under standard conditions to address the reproducibility of these phenomena (PEG 3400, 1% strain, in the presence of 0.2 mM ATP), providing the basis for the subsequent quantitative analysis of the oscillatory behavior (Table 1). The frequency of oscillations was independent of the applied shear strain in the range of 0.5–2%. In addition, the relative amplitude (G′/G′ max) and frequency of the oscillations remained unaffected by changes in the PEG actin dimer chain length (crosslinker), although an increase in G′ was observed (Fig. 2).

Table 1 Qualitative evaluation of mechanical oscillations in F-actin hydrogels under various chemical and mechanical conditions

Condition	Range or parameter	Oscillation period
Crosslinker length	PEG 3400–10 000	Independent
Applied shear strain	0.5–2.0%	Independent
ATP concentration	0.2–2.0 mM	Independent
Dimer concentration	>2.7%	Independent
Crosslinker (dimer)	0% (none)	N/A
Effect of phalloidin	200 µM	N/A

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Fig. 2 (A) Time profiles of relative G′ after PEG-crosslinked G-actin polymerisation. (B) The corresponding power spectra. Molecular weight of PEG in the PEG actin dimer: 3400 (red) and 20 000 (blue). G′ was measured at a shear strain of 1.0 Hz. The power spectra were calculated using the Microcal Origin 8 software.

Fig. 3 shows the time profiles of G′ when G-actin was polymerised under different PEG actin dimer concentrations.¹³ We observed a clear qualitative trend in the oscillation behaviour: the oscillation amplitude diminished markedly as the PEG actin dimer concentration decreased (Fig. 3A–D). In each case, G′ increased rapidly during polymerisation, while the G′ of the F-actin gel substantially decreased at lower crosslinker concentrations, indicating substantially reduced crosslinking density. Notably, the oscillation amplitude decreased markedly as the PEG actin dimer concentration decreased (Fig. 3A–D). The mean oscillation amplitudes were 238 ± 49 Pa, 26.0 ± 3.9 Pa, and 10.6 ± 2.7 Pa for PEG actin dimer concentrations of 10.6%, 5.3%, and 2.7%, respectively. The oscillation disappeared entirely in the absence of a crosslinker, i.e. in the case of F-actin solution (Fig. 3E). Thus, the oscillation is strongly associated with the crosslinking density (Fig. 3) and experimentally demonstrates that chemical crosslinking is essential for the emergence of autonomous oscillation. Power spectrum analysis using the data in Fig. 3A revealed that the G′ of the actin hydrogel oscillates as a typical reverse-sawtooth waveform with a frequency of 0.0006 Hz (Fig. S2). We propose that the driving force behind these oscillations is the chemo-mechanical coupling between actin treadmilling and the mechanical constraints of the network. Treadmill polymerization within a constrained network likely leads to the accumulation of torsional strain. As F-actin is known to be fragile toward torsional deformation, the accumulated strain eventually triggers a cooperative breakdown (depolymerization) of the filaments, resulting in the observed rapid decay in G′.

Fig. 3 Time profiles of G′ by G-actin polymerisation under different PEG 3400 actin dimer concentrations: A, 10.6%; B, 5.3%; C, 2.7%; D, 1.3%; E, 0%; and F, 10.6% in the presence of 200 μM phalloidin. G′ was measured at a shear strain of 1.0% and a frequency of 1.0 Hz. Panels (A), (D), (E) and (F) were recalculated and adapted with permission from ref. 13. Copyright 2016 Springer Nature.

A plausible mechanism for the observed oscillation is the sequential polymerising–depolymerising of the crosslinked F-actin called “treadmilling”.⁹ Treadmilling refers to the cascade-type chemical dynamics of adding (polymerising) and deleting (depolymerising) G-actin subunits of the F-actin filament, accompanied by adenosine triphosphate (ATP) decomposition. Owing to the intrinsic polarity of F-actin, polymerisation occurs preferentially at the plus end, while depolymerisation predominates at the minus end. When F-actin reaches a steady state (non-equilibrium), both polymerisation and depolymerisation rates become equal, and no change in the length of F-actin occurs. During this process, locomotion by G-actin treadmilling is observed, depending sensitively on environmental conditions. If the observed oscillation in the F-actin gel is associated with the treadmilling dynamics of the gel, then it should be suppressed by phalloidin, which is a strong inhibitor of the depolymerisation of F-actin.¹⁵ As shown in Fig. 3F, the presence of 200 µM phalloidin completely abolished the oscillations, confirming that they originate from treadmilling dynamics. Notably, the base G′ value in the presence of phalloidin was substantially lower than that of the control (Fig. 3A). We propose that phalloidin stabilizes the polymerization nuclei, leading to an increase in the number of nucleation sites and the formation of shorter F-actins. Because treadmilling is dominated by the equilibrium concentration of surrounding ATP, changes in ATP levels were expected to influence the characteristics of the oscillation. Fig. 4 shows the oscillation profiles when ATP concentration was changed. G′ and the amplitude of the oscillation were substantially changed, suggesting sensitive and complex dynamics of the treadmilling equilibrium of ATP. Thus, the chemical dynamics of treadmilling could be concluded as a possible origin of the observed mechanical oscillation, where the presence of the crosslinked network is essential. We propose that the driving force behind these oscillations is the chemo-mechanical coupling between actin treadmilling and the mechanical constraints of the network. Treadmill polymerization within a constrained network likely leads to the accumulation of torsional strain. As F-actin is known to be fragile toward torsional deformation, the accumulated strain eventually triggers a cooperative breakdown (depolymerization) of the filaments, resulting in the observed rapid decay in G′.

Fig. 4 Time profiles of G′ by PEG 3400-crosslinked G-actin polymerisation at different concentrations of ATP.

Notably, assessing whether the autonomous oscillation originating from the treadmilling equilibriums represents physical or chemical waves is crucial. If the oscillatory change in G′ is induced by periodical hydrodynamic waves coupled with the treadmilling dynamics, then the wave would be of a physical nature. Conversely, if the oscillation of G′ stems from chemical waves, such as the periodic concentration changes of ions (or other chemical components) coupled with the dynamics of ATP hydrolysis, then the wave would be of a chemical nature. Changes in the ion concentration reportedly cause variations in the size and mechanical properties of water-swollen hydrogels. In either case, the nano-ordered wave should be amplified and synchronised via diffusion in the crosslinked network of the gel to obtain periodic mechanical oscillations of hundreds of Pa. However, at present, sufficient data to discuss this aspect in detail are lacking, and further studies are necessary.

A similar chemo-mechanical oscillation of G′ was observed in crosslinked microtubule (MT) hydrogels (Fig. 5). MTs, another class of cytoskeletal proteins, form cylindrical assemblies of tubulins through simultaneous polymerisation.^16,17 As shown in Fig. 5, the three-dimensional MT gel showed continuous oscillation of constant amplitude for more than 1 h. Temporal oscillations of MTs during polymerisation caused by dynamic instability, which includes rapid switching between phases of growth and shrinkage at the ends of the MTs, have been reported previously,¹⁸ but in the absence of crosslinking, these oscillators decayed and disappeared within 25 min after the polymerisation started, suggesting that the underlying mechanism fundamentally differs from our observations. The comparative observation of crosslinked MT gels suggests that while chemical crosslinking is essential for synchronizing protein dynamics into macroscopic oscillations, the stability and patterns of these oscillations are likely determined by the intrinsic mechanics of the constituent filaments—specifically, the torsional fragility of F-actin versus the end-wise dynamic instability of MTs.

Fig. 5 Time profiles of G′ by PEG-crosslinked tubulin polymerisation. G′ values were measured at 1 Hz under 1% strain. The temperature was increased to 37 °C and tubulin polymerisation was initiated at the point indicated by the red arrow (5 min).

The autonomous oscillation observed here provides a new possibility for a simple gel oscillator. Therefore, we attempted to elucidate the oscillation mechanism by identifying the chemo-mechanical coupling process in the F-actin gel, focusing particularly on the role of the network in synchronising dynamic behaviour. First, we investigate why the network structure is essential for the emergence of synchronized oscillations and define its specific role within the gel oscillator.

Several studies have shown that hydrogels can emulate non-linear collective chemical reactions and give rise to temporal oscillations and pattern formation.^19–21 For example, the introduction of the Belousov–Zhabotinsky reaction components into hydrogels induced periodic oscillations together with swelling–deswelling repetitive volume changes.^22,23 These systems exhibit unique chemical diffusion dynamics; hydrogels below a critical radius do not chemically oscillate due to insufficient diffusion kinetics of the fluid.²⁴ Ionised gels can act as DC → AC converters displaying repetitive current oscillations (0.01–0.2 Hz) with higher harmonics when a constant electric potential is applied.^25,26 Gels are inherently dynamic systems, with crosslinked networks undergoing continuous and vigorous thermal vibrations with a wide range of natural frequencies.^27–29 Quasi-elastic light scattering offers direct experimental access to the wavelengths and lifetimes of these vibrations, revealing that their frequency strongly depends on the rigidity and segmental size between two junction nodes, which predominate viscoelastic behaviour.^14,30 Such a broad range of vibrations allow crosslinked gels to preserve elastic energy by coupling with each other. Consequently, when an internal or external vibration occurs, it can adjust the rhythms via coupling with a broad range of dynamic vibrations to cause synchronisation.^19,27,31,32 Thus, synchronised mechanical oscillation may emerge when the frequency of internal vibrations originating from the treadmilling coincides with the thermal vibration of the network at a resonant frequency. Therefore, the transmission of the vibration through the network is important to couple with treadmilling dynamics at the resonant frequency, and the viscoelastic properties of the water in the network will determine the resonance frequency of vibration. Conversely, in systems without crosslinking, in which macromolecules are statistically dispersed in the fluid, internal vibrations originating from treadmilling equilibrium are mostly dissipated due to fluctuations or the interference of multiple random waves. Such an example is the F-actin solution with 0% crosslinker (Fig. 3E), where transmission of the vibration via crosslinking cannot occur.

Next, we examined the role of the highly ordered structure of the network in displaying synchronised oscillations. Emergence is often caused by the newly organised hierarchical structure, resulting in a non-linear and less stable ensemble of dynamics at a constituent level.^3–5 The constituent F-actin is 6 nm in diameter with a helical periodicity of 72 nm^33,34 and a persistence length of ∼10 µm.³⁵ It forms parallel right-handed double-stranded coiled-coil bundles that are very rigid and robust.³⁵ Our F-actin gel consists of newly polymerised, young filaments and rigid stranded bundles that almost simultaneously form a hierarchical network structure during polymerisation. Electron microscopy studies revealed that young F-actin exhibits less stable intermolecular structures and greater structural plasticity than canonical F-actin. A kinetic assay by Mitchison et al. also demonstrated that young F-actin depolymerises faster than aged filaments.^36,37 These results show that the F-actin gel consisting of a newly ordered young network may enhance structural plasticity and facilitate synchronised chemo-mechanical response. In addition, rigid and robust network bundles are highly cooperative. As demonstrated previously,⁸ the F-actin gel exhibits highly cooperative responses to external stimuli and suggests the presence of strong interactions between component chains. Unlike chemical gels, wherein a single polymer chain is randomly crosslinked, the cooperative coupling of a wide range of vibrations in cytoskeletal protein gels enhances the preservation of the energy required to achieve synchronised oscillation. The harmonised inchworm-like waving motion of the F-actin gel on the myosin gel might be a result of highly synchronised integrity and motility.^38,39 Conversely, synthetic polymer gels consist of a very flexible and statically crosslinked network, lacking such dynamic cooperativity. The distinct behaviour of bio-derived hydrogels introduces a new scientific paradigm for designing and fabricating novel oscillating materials, such as autonomous, communicating, and motile “soft and wet” systems capable of emergent behaviour without requiring complex technically demanding methods.

Experimental

Preparation of the PEG-crosslinked actin hydrogel

The PEG-crosslinked G-actin (PEG actin dimer) hydrogel was prepared as described previously.⁸ In brief, G-actin (8 mg mL⁻¹) in G-buffer (1 mM sodium bicarbonate, 0.1 mM CaCl₂, and 0.2 mM ATP) was reacted with 0.5 molar equivalents of bis-maleimide-terminated PEG (MW 3400 or 20 000; SUNBRIGHT, NOF-Corporation, Japan) for 2 h at room temperature, then the reaction mixture was incubated at 4 °C. Actin polymerisation was performed by adding a NaCl solution to a final concentration of 0.3 M, achieving a final actin concentration of 5 mg mL⁻¹, followed by incubation at 25 °C on a rheometer. The PEG actin dimer solution was diluted with an uncrosslinked G-actin solution before polymerisation to evaluate the effect of PEG actin dimer concentration on oscillation. The PEG actin dimer content was determined by SDS-PAGE, as described previously.⁸

Preparation of the PEG-crosslinked MT hydrogel

Tubulin was purified from porcine brain as reported previously.^16,17 PEG-crosslinked tubulin was prepared following established protocols. MTs were polymerised from tubulin (10 mg mL⁻¹) in a polymerisation buffer (80 mM PIPES, 1 mM EGTA, 6 mM MgCl₂, and 5 mM GTP; pH adjusted to 6.8 using KOH) at 37 °C for 30 min. Bis-N-hydroxysuccinimidylester PEG (MW: 5000; SUNBRIGHT DE-050GS, NOF-Corporation, Japan) as a crosslinker was added to the tubulin solution at a tubulin : crosslinker molar ratio of 2 : 1, which corresponds to a molar ratio of the NHS group to tubulin of 1 (NHS/tubulin = 1). The crosslinking reaction proceeded at 37 °C for 2 h to yield an intact MT gel. The MT gel was depolymerised to a sol by cooling on ice for 15 min. PEG-crosslinked tubulin was then placed on a rheometer and cooled to 0 °C. Five minutes after starting the measurement, the temperature was increased to 37 °C to initiate tubulin polymerisation.

Rheological experiments

The viscoelastic properties of the hydrogels were examined using an oscillating rheometer (AR-G2, TA Instruments) as described previously.^8,15 The power spectra were calculated using the Microcal Origin 8 software.

Conclusions

In this study, we demonstrated that chemically crosslinked F-actin hydrogels exhibit autonomous, long-lasting, and synchronized mechanical oscillations during self-organized polymerization. Our quantitative analysis reveals that these oscillations are driven by a feedback loop involving the accumulation and periodic cooperative release of torsional strain within the PEG-crosslinked hierarchical network. The essential role of the crosslinked architecture was experimentally confirmed by the complete disappearance of oscillations in uncrosslinked solutions. Furthermore, the unexpected decrease in elasticity and suppression of oscillations by phalloidin underscore the necessity of dynamic, cooperative filament turnover and optimal filament length for mechanical output. These findings introduce a new paradigm for designing autonomous and motile “soft and wet” materials, where biological components generate life-like emergent behavior through structural and chemical synergy.

Author contributions

K. S. and R. K. contributed to investigation, data curation, conceptualisation and writing – review and editing. Y. O. contributed to conceptualisation, supervision, and writing – original draft. All authors have approved the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

Raw data are available from K. S. upon request.

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information includes the time profiles of storage and loss moduli (Fig. S1), power spectral analyses under various conditions (Fig. S2), and further rheological details. See DOI: https://doi.org/10.1039/d5sm01205h.

Acknowledgements

This work was partially supported by a JSPS KAKENHI grants awarded to K. S. (24K08605) and R. K. (23K04556). We thank Editage for editing the manuscript.

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