A neuromechanical model for Drosophila larval crawling based on physical measurements.

BACKGROUND: Animal locomotion requires dynamic interactions between neural circuits, the body (typically muscles), and surrounding environments. While the neural circuitry of movement has been intensively studied, how these outputs are integrated with body mechanics (neuromechanics) is less clear, in part due to the lack of understanding of the biomechanical properties of animal bodies. Here, we propose an integrated neuromechanical model of movement based on physical measurements by taking Drosophila larvae as a model of soft-bodied animals. RESULTS: We first characterized the kinematics of forward crawling in Drosophila larvae at a segmental and whole-body level. We then characterized the biomechanical parameters of fly larvae, namely the contraction forces generated by neural activity, and passive elastic and viscosity of the larval body using a stress-relaxation test. We established a mathematical neuromechanical model based on the physical measurements described above, obtaining seven kinematic values characterizing crawling locomotion. By optimizing the parameters in the neural circuit, our neuromechanical model succeeded in quantitatively reproducing the kinematics of larval locomotion that were obtained experimentally. This model could reproduce the observation of optogenetic studies reported previously. The model predicted that peristaltic locomotion could be exhibited in a low-friction condition. Analysis of floating larvae provided results consistent with this prediction. Furthermore, the model predicted a significant contribution of intersegmental connections in the central nervous system, which contrasts with a previous study. This hypothesis allowed us to make a testable prediction for the variability in intersegmental connection in sister species of the genus Drosophila. CONCLUSIONS: We generated a neurochemical model based on physical measurement to provide a new foundation to study locomotion in soft-bodied animals and soft robot engineering.

Fracture Behavior of Polyrotaxane-Toughened Poly(Methyl Methacrylate).

The fracture behavior of polyrotaxane (PR)-modified poly(methyl methacrylate) (PMMA) was investigated. PR is a supramolecule with rings threaded onto a linear backbone chain, which is capped by bulky end groups to prevent the rings from de-threading. The ring structure is α-cyclodextrin (CD), and it can be functionalized to enhance its affinity with the hosting polymer matrix. Adding only 1 wt % of PR containing methacrylate functional groups (mPR) at the terminal of some of the polycaprolactone-grafted chains on CD promotes massive crazing, resulting in a significant improvement in fracture toughness while maintaining the modulus and transparency of the PMMA matrix. Dynamic mechanical analysis and atomic force microscopy studies reveal that mPR strongly interact with PMMA, leading to higher molecular mobility and enhanced molecular cooperativity during deformation. This molecular cooperativity may be responsible for the formation of massive crazing in a PMMA matrix, which leads to greatly improved fracture toughness.

Adhesion Force Analysis of Dynamic Polymer Brushes.

Spontaneous surface segregation of amphiphilic diblock copolymers at the water interface from the elastomeric portion was utilized for the fabrication of hydrophilic brushes, named as "dynamic polymer brush". Observation of the dynamic polymer brushes appears only when immersed in water and demands advanced experimental techniques for embedded interfaces such as neutron reflectivity. Measurement of the hydrophobic interaction at the polymer/water interface is not only an alternative method to monitor the brush but also reveals its unique surface properties. We carried out adhesion force measurements using atomic force microscopy with a hydrophobic probe for measuring the hydrophobic interactions of dynamic polymer brushes in water. Dynamic polymer brushes showed reduced hydrophobic interaction, which becomes more significant at higher graft density. Moreover, a unique transitional response to the applied pressure was observed for the dynamic polymer brush: the adhesion force was almost zero at low applied pressure and increased by further increasing the applied pressure. This phenomenon may indicate reallocation or retraction of the block copolymer chains from the contact area by the applied pressure, which are the unique characteristics of nonbound dynamic polymer brush chains. We also conducted adhesion force imaging and proved that dynamic polymer brushes form uniform layers without any defects, irrespective of brush density, which suggests that the interaction between the dynamic polymer brush chains is that of repulsion.

Interfacial Energy Measurement on the Reconstructive Polymer Surface: Dynamic Polymer Brush by Segregation of Amphiphilic Block Copolymers.

Herein, the interfacial energy of a reconstructive polymer surface formed by segregation is analyzed by measuring the change in the size of elastomer thin films floating on water. When a system in which amphiphilic diblock copolymers are mixed with the hydrophobic elastomer is in contact with water, surface reconstruction is triggered by the segregation of copolymers with a gain in the hydration energy of the hydrophilic blocks. The hydrophilic brush layer spontaneously formed at the elastomer-water interface is named the dynamic polymer brush. Although it is anticipated that the interfacial energy will significantly decrease in the dynamic polymer brush system, a direct measurement of the interfacial energy of the reconstructive interface is a challenge. We propose a novel method to measure the interfacial energy of a reconstructive polymer surface by measuring the deformation of elastomer thin films floating on water and apply it to the dynamic polymer brush system. The interfacial energy of the dynamic polymer brush formed by the segregation of amphiphilic diblock copolymers with longer hydrophilic chains drastically decreased to zero due to the high hydration energy of hydrophilic chains. Based on the neutron reflectometry results, the graft density and thickness of the dynamic polymer brush system floating on water were found to be lower than those of the system fixed onto solid substrates. This indicates that the floating system can respond to an external environment with a high degree of freedom (graft density, brush thickness, and interface area).

Precise control of cyclodextrin-based pseudo-polyrotaxane lamellar structure via axis polymer composition.

Self-assembly of cyclodextrin (CD) with guest polymers has attracted much attention owing to its biocompatibility and accessibility. In this study, we investigate the composition effect of poly(ethylene oxide)m-b-poly(propylene oxide)n-b-poly(ethylene oxide)m (EOmPOnEOm) triblock copolymers on lamellar or plate structures formed by complexation with ß-CD. EO5PO29EO5, EO14PO29EO14, and EO75PO29EO75 show periodic lamellar morphology consisting of single-crystalline pseudo-polyrotaxane (PPR) nanosheets with a thickness equal to the central PO length. This is because ß-CDs selectively cover the PO component and cause the microphase separation between ß-CD and EO layers. The thickness of the EO layers increases linearly with increasing number of EO units, which suggests that the EO chains are constrained into virtual cylinders with the diameter of the ß-CD. This means that we can precisely control the thickness of both the crystal (ß-CD and PO) and the amorphous (EO) layers in the lamellar structure. In contrast, EO2PO29EO2 forms a thin plate structure, where not only PO but also EO chains are covered with ß-CD. Furthermore, the length of the central PO component is necessary to form the lamellar structure with the phase separation between the ß-CD and EO layers. These findings provide a more fundamental understanding to enhance the variety and applicability of CD-based self-assembled materials.

Prolonged Glass Transition due to Topological Constraints in Polyrotaxanes.

Topological constraints in polyrotaxanes significantly affected their glass transition dynamics. The effects of the constraints were systematically studied using a series of different coverage glass-forming polyrotaxanes consisting of a common polymer and threaded ring molecule of varying ratios. Although their ratios were similar and hence exhibited similar Tg values by differential thermal analysis, mechanical relaxation was considerably prolonged with increasing coverage. The relaxation became a two-step process: a faster step at a common temperature near the Tg and another which was prolonged by the coverage increase. Relaxation dynamics analysis revealed that segment motions, which are cooperative translations of different components, freeze at considerably higher temperatures than the Tg with increasing coverage. This suggests that although the rings are released from conventional interactions at the Tg, their cooperative translational motions are significantly constrained by the threading polymers with increasing coverage.

Molecular Dynamics of Polyrotaxane in Solution Investigated by Quasi-Elastic Neutron Scattering and Molecular Dynamics Simulation: Sliding Motion of Rings on Polymer.

In this study, we investigated the molecular dynamics of polyrotaxane (PR), composed of α-cyclodextrins (CDs) and a poly(ethylene glycol) (PEG) axial chain, in solution by means of quasi-elastic neutron scattering (QENS) measurements and full-atomistic molecular dynamics (MD) simulations. From QENS experiments, we estimated the diffusion coefficients of CD and PEG monomers in PR, which are in quantitative agreement with those obtained by MD simulations. By analyzing the simulation results, we succeeded, for the first time, in observing and quantifying the sliding motion of CD along a PEG chain. The diffusion coefficient for the sliding motion is almost 6 times lower than that of the translational diffusion of CD in PR at room temperature. The retardation of the sliding motion is caused by the energy barrier on PEG produced by molecular interactions between CD and PEG. We propose a simple equation to describe the diffusion coefficient of the sliding dynamics in PR by combining the Einstein-Stokes diffusion model and a one-dimensional jump diffusion model. This work provides a general strategy for the molecular designs to control the sliding motion in PR.

Polyrotaxane Brushes Dynamically Formed at a Water/Elastomer Interface.

Dense polymer brushes with closely packed rotaxane structures were formed at the interface of water and a styrene-butadiene elastomer by spontaneous segregation of an amphiphilic polyrotaxane (PR), a mechanically interlocked polymer consisting of hydrophobic polybutadiene threading through multiple hydrophilic γ-cyclodextrin (γ-CD) derivatives. Segregation of PR at the water/elastomer interface was suggested by X-ray photoelectron spectroscopy. The polymer brush structure at the water interface was investigated using neutron reflectometry. Brush structures were found to depend on the number of CDs on the PRs; the PR with a small number of CDs formed a thinner and homogeneous brush, whereas the PR with a higher number of CDs formed a thicker and less-ordered brush. These PR-brushes showed protein repulsion, resulting from the surface-hydrated brush layer preventing direct contact of proteins.

Pronounced effects of the densities of threaded rings on the strain-dependent Poisson's ratio of polyrotaxane gels with movable cross-links.

The density of threaded ring molecules (fCD) in polyrotaxane (PR) chains has pronounced effects on the strain-induced swelling of PR gels where the cross-linked ring molecules are slidable along the network strands. The equilibrium Poisson's ratio (µ∞), which is a measure of the strain-induced volume change, for the PR gel increases with an increase in elongation (λ) at moderate λ but becomes a constant value () at sufficiently large λ. When the modulus exceeds a threshold value (Ec), the λ dependence of µ∞ disappears due to the loss of the slidability of the cross-links. The fraction fCD significantly influences the values of and Ec. When fCD is sufficiently small (<14%), (≈0.25) agrees with the values of µ∞ for the classical gels in good solvents. When fCD is high (>25%), varies over a wide range (0.22 < < 0.33) depending on fCD and the cross-link concentration in a complicated way. The modulus Ec at fCD = 25% is more than twice as high as that at fCD = 5% due to the finite contribution of the larger amount of uncross-linked ring molecules via combinatorial entropy in the axial polymers. The origin of the markedly small values of µ∞ (less than 0.1) at small λ is also considered on the basis of the magnitude of the accompanying force reduction caused by the slidable function of the cross-links.

A thermoresponsive dynamic polymer brush fabricated by the segregation of amphiphilic diblock copolymers.

A highly dense polymer brush was previously fabricated by the spontaneous segregation of amphiphilic diblock copolymers in an elastomer matrix into water and a hydrophobic polymer interface and named a 'dynamic polymer brush'. We fabricated a lower critical solution temperature (LCST)-type thermoresponsive dynamic polymer brush by mixing polyisoprene-b-poly[tri(ethylene glycol)methyl ether methacrylate] (PI-b-PME3MA) into a polystyrene-b-polyisoprene-b-polystyrene (SIS) elastomer. The LCST of PME3MA in water is 52 °C. The structure of the polymer brush was determined at several different temperatures using neutron reflectivity. With increasing temperature, the brush thickness of the LCST-type thermoresponsive dynamic polymer brush decreases, similar to the conventional fixed brush with the LCST-type thermoresponse. However, the graft density of the dynamic polymer brush surprisingly increases with increasing temperature. The change of the brush density of the conventional fixed polymer brush is not allowed. However, we observed for the first time that dynamic polymer brushes uniquely respond to increasing temperature with increasing brush densities.

Quantitative Analysis of Polymer Brush Formation Kinetics Using Quartz Crystal Microbalance: Viscoelasticity of Polymer Brush.

Polymer brush formation kinetics was measured by quartz crystal microbalance (QCM). In the QCM measurement anomalous complex frequency shift as a function of graft density was observed: dissipation rate shift ΔΓ first increased, showed a peak, and then decreased despite the graft density of the polymer brush was increasing monotonically. We calculated the shear modulus of the brush layer from the measured complex frequency shift and revealed that the peak of ΔΓ described the crossover from a viscous brush layer to elastic brush layer. The crossover for the poly(ethylene glycol) with a molecular weight of 2000 occurs at around the characteristic graft density of 0.17 chains/nm2 which was revealed from the structure analysis by surface plasmon resonance (SPR) and neutron reflectivity (NR).

Slide-Ring Materials Using Cyclodextrin.

We have recently synthesized slide-ring materials using cyclodextrin by cross-linking polyrotaxanes, a typical supramolecule. The slide-ring materials have polymer chains with bulky end groups topologically interlocked by figure-of-eight shaped junctions. This indicates that the cross-links can pass through the polymer chains similar to pulleys to relax the tension of the backbone polymer chains. The slide-ring materials also differ from conventional polymers in that the entropy of rings affects the elasticity. As a result, the slide-ring materials show quite small Young's modulus not proportional to the cross-linking density. This concept can be applied to a wide variety of polymeric materials as well as gels. In particular, the slide-ring materials show remarkable scratch-proof properties for coating materials for automobiles, cell phones, mobile computers, and so on. Further current applications include vibration-proof insulation materials for sound speakers, highly abrasive polishing media, dielectric actuators, and so on.

Synthesis, structure, and mechanical properties of silica nanocomposite polyrotaxane gels.

A significantly soft and tough nanocomposite gel was realized by a novel network formed using cyclodextrin-based polyrotaxanes. Covalent bond formation between the cyclic components of polyrotaxanes and the surface of silica nanoparticles (15 nm diameter) resulted in an infinite network structure without direct bonds between the main chain polymer and the silica. Small-angle X-ray scattering revealed that the homogeneous distribution of silica nanoparticles in solution was maintained in the gel state. Such homogeneous nanocomposite gels were obtained with at least 30 wt % silica content, and the Young's modulus increased with silica content. Gelation did not occur without silica. This suggests that the silica nanoparticles behave as cross-linkers. Viscoelastic measurements of the nanocomposite gels showed no stress relaxation regardless of the silica content for <20% compression strain, indicating an infinite stable network without physical cross-links that have finite lifetime. On the other hand, the infinite network exhibited an abnormally low Young's modulus, ~1 kPa, which is not explainable by traditional rubber theory. In addition, the composite gels were tough enough to completely maintain the network structure under 80% compression strain. These toughness and softness properties are attributable to both the characteristic sliding of polymer chains through the immobilized cyclodextrins on the silica nanoparticle and the entropic contribution of the cyclic components to the elasticity of the gels.

Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation.

The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

Synthesis of graft polyrotaxane by simultaneous capping of backbone and grafting from rings of pseudo-polyrotaxane.

Graft polyrotaxanes, with poly(ε-caprolactone) (PCL) graft chains on the ring components were synthesized by the simultaneous ring-opening polymerization of ε-caprolactone from both ends of the backbone polymer, an end-functionalized polyethylene glycol (PEG) and the formation of inclusion complexes with α-cyclodextrin (α-CD). PEG with multiple functional groups at each end was prepared by the condensation of PEG-amine and D-gluconic acid; the PEG derivative formed an inclusion complex with α-CD. The polymerization of multiple hydroxy groups at the backbone ends resulted in a star-shaped end group, which served as a bulky capping group to prevent dethreading. In contrast, PEG with only one hydroxy group at each end did not produce polyrotaxanes, indicating that single PCL chains were too thin to confine α-CDs to the complex. In addition, the grafting polymerization proceeded properly only when robust hydrogen bonds formed between α-CDs were dissociated using a basic catalyst. Since the dissociation also induced dethreading, kinetic control of the polymerization and dissociation were crucial for producing graft polyrotaxanes. Consequently, this three-step reaction yielded graft polyrotaxanes in a good yield, demonstrating a significant simplification of the synthesis of graft polyrotaxanes.

Strain-Induced Orientation of Host Rings that Determines the Sliding of Guest Polymers and Plasticity of Glassy Polyrotaxane.

The unique motility of mechanically interlocked polymers enables their mechanical properties to profoundly transform. This property has been exploited less in glassy materials than in rubbery materials. This study demonstrated that in the glassy state the rings must orient before sliding and clarified the requisite structural changes by the synchrotron microbeam X-ray diffraction mapping of a ductile cyclodextrin (CD)-based glassy polyrotaxane. After inducing neck formation and propagation by uniaxial tension, the strain-localized area was scanned, elucidating how the CD orientation and its correlation distance change. As necking approaches and local strain increases, the CD rotational axis orients considerably in the tensile direction. Near the neck inflection point, polymer sliding triggers a sudden structural transformation, forming a phase-separated structure between the CDs and polymers that toughens the neck. This strain-induced orientation preceding sliding appears to facilitate sliding. In the rubbery state, host molecules can orient freely with the guest polymer orientation, but glassy materials must be designed to facilitate host orientation to enable guest sliding with minimum molecular friction.

Cross-Linking-Filler Composite Materials of Functionalized Hexagonal Boron Nitride and Polyrotaxane Elastomer.

This study demonstrates cross-linking-filler composites in which covalent bonds between the fillers and polymer chains act as the main cross-linking points for the development of flexible and thermally conductive materials. Cross-linking-filler composites are fabricated using functionalized hexagonal boron nitride (hBN) fillers and polyrotaxane, called slide-ring polymers. The hBN particles modified with a carbon layer were produced by plasma processing in hydroquinone aqueous solution and functionalized with isocyanate groups. As the functionalized hBN provides cross-linking points for polyrotaxane, the cross-linking-filler composites can reduce cross-linking agents among polyrotaxane and exhibit considerable flexibility. Young's moduli of the cross-linking-filler composites are much lower than those of previously reported polyrotaxane composites while retaining their toughness. These values are relatively close to those of unfilled polyrotaxane elastomers, despite containing hBN fillers with a content of 50 wt %. Thus, the cross-linking-filler composites exhibit a combination of flexibility and thermal conductivity, which few hBN/elastomer composites have achieved.

Strain-induced crystallization and phase separation used for fabricating a tough and stiff slide-ring solid polymer electrolyte.

The demand for mechanically robust polymer-based electrolytes is increasing for applications to wearable devices. Young's modulus and breaking energy are essential parameters for describing the mechanical reliability of electrolytes. The former plays a vital role in suppressing the short circuit during charge-discharge, while the latter indicates crack propagation resistance. However, polymer electrolytes with high Young's moduli are generally brittle. In this study, a tough slide-ring solid polymer electrolyte (SR-SPE) breaking through this trade-off between stiffness and toughness is designed on the basis of strain-induced crystallization (SIC) and phase separation. SIC makes the material highly tough (breaking energy, 80 to 100 megajoules per cubic meter). Phase separation in the polymer enhanced stiffness (Young's modulus, 10 to 70 megapascals). The combined effect of phase separation and SIC made SR-SPE tough and stiff, while these mechanisms do not impair ionic conductivity. This SIC strategy could be combined with other toughening mechanisms to design tough polymer gel materials.

Bioinspired Oxidation-Resistant Catechol-like Sliding Ring Polyrotaxane Hydrogels.

Adaptable hydrogels have been used in the biomedical field to address several pathologies, especially those regarding tissue defects. Here, we describe unprecedented catechol-like functionalized polyrotaxane (PR) polymers able to form hydrogels. PR were functionalized with the incorporation of hydroxypyridinone (HOPO) moieties into the polymer backbone, with a degree of substitution from 4 to 22%, depending on the PR type. The hydrogels form through the functionalized supramolecular systems when in contact with a Fe(III) solution. Despite the hydrogel formation being at physiological pH (7.4), the HOPO derivatives are extremely resistant to oxidation, unlike common catechols; consequently, they prevent the formation of quinones, which can lead to irreversible bounds within the matrix. The resulting hydrogels demonstrated properties lead to unique hydrogels with improved mechanical behavior obtained by metallic coordination crosslinking, due to the synergies of the sliding-ring PR and the non-covalent (reversible) catechol analogues. Following this strategy, we successfully developed innovative, cytocompatible, oxidative-resistant, and reversible crosslinked hydrogels, with the potential of being used as structural self-materials for a variety of applications, including in the biomedical field.

High-yield one-pot synthesis of polyrotaxanes with tunable well-defined threading ratios over a wide range.

In this work, we report a high-yield one-pot synthesis of polyrotaxane (PR), composed of (2-hydroxypropyl)-α-cyclodextrin (hpCD) and polyethylene glycol (PEG), with well-defined hpCD threading ratios controllable across a wide range from 0.64% to 10%. In hpCD/PEG aqueous solutions, hpCDs are well dispersed and threaded spontaneously into hpCDs to form a pseudo-PR (pPR) structure. The homogeneous dispersion of hpCDs results in a well-defined threading ratio of hpCDs on PEG, which is suggested by the fact that the dispersity of the molecular weight distribution of PR is almost the same as that of pure PEG. The well-defined hpCD threading ratio of the PRs can be controlled over a wide range by tuning the hpCD concentration in the pPR solutions.