DOI: 10.5061/dryad.zpc866tjq
title: Tetanus-driven biohybrid multi-joint robots powered by muscle rings with enhanced contractile force

description: Biohybrid actuators utilizing muscle rings have been limited to twitching
 movements and are unsuitable for sustained contractile force applications.
 In this study, we developed muscle rings capable of generating high
 contractile forces under tetanus stimulation. By enhancing the rigidity of
 pillar-shaped supports and increasing myoblast density through reduced
 extracellular matrix, we promote the formation of dense, well-aligned
 muscle fiber bundles. The optimized muscle rings exhibit significantly
 higher contractile forces compared to traditional methods. Integrating
 these muscle rings with C-shaped anchors efficiently converts contractile
 force into bending motion. We demonstrate the application of these muscle
 rings in gripper and slither-type biohybrid robots, achieving large
 deformation and undulatory movement. This work advances biohybrid robotics
 by enabling sophisticated movements requiring continuous and powerful
 muscle contractions.
description: # Tetanus-driven biohybrid multi-joint robots powered by muscle rings with
 enhanced contractile force
 [https://doi.org/10.5061/dryad.zpc866tjq](https://doi.org/10.5061/dryad.zpc866tjq) ## Abstract Biohybrid actuators using muscle rings have typically been limited to twitching movements. In this study, we develop muscle rings that generate high contractile forces under tetanus stimulation by increasing support rigidity and myoblast density. These optimized muscle rings produced stronger forces and, when combined with C-shaped anchors, efficiently converted contraction into bending motion. We applied them to gripper and slither-type robots, enabling large deformation and continuous movement, advancing biohybrid robotics toward more powerful and sustained actuation. This dataset represents the results of the experiments in this study. The file name corresponds to the figure number in the main text or the supplementary. ## Description of the data and file structure ### Purposes of all files #### Fig. 2: **Morphological and functional evaluation of the muscle rings.** * File Fig.2B.xlsx : Width changes of the muscle rings over culture days. * File Fig.2C.xlsx : Displacement of a tracking point (P) placed on a muscle ring with electrically responsive contraction. * File Fig.2D.xlsx : Active force and passive force of the muscle ring with applied strain. * File Fig.2G.xlsx : Contractile force of the muscle rings cultured on pillar-shaped supporters with different stiffnesses. * File Fig.2I.xlsx : The relationship between the amount of ECM and the contractile force of muscle rings (applying different strain). * File Fig.2J.xlsx : Contractile force against ECM amount. * File Fig.2K.xlsx : Contractile force of muscle rings with different cell densities. * File Fig.2L.xlsx : Temporal change in contractile force under different electric frequencies. * File Fig.2M.xlsx : Contractile force against electric frequency. * File Fig.2N.xlsx : Contractile force under different electric field intensities. ### Fig. 3: Evaluation of the biohybrid unit actuator powered by muscle rings. * File Fig.3C.xlsx : Displacement of a tracking point P-P’ in Z direction placed on a biohybrid unit actuator under various electric field frequencies.   - File Fig.3E.xlsx : Comparison of the contractile force of muscle strips and muscle rings under identical electric field application (1.7 V/mm). * File Fig.3F.xlsx : The kinking angle between the C-shaped anchors and the muscle tissues. - File Fig.3G.xlsx : Comparison of the bending angle of the substrate between the biohybrid unit actuators driven by muscle strips and those driven by muscle rings. * File Fig.3I.xlsx : Comparison of the bending angles of the biohybrid unit actuators whose anchors were applied with different surface coatings. * File Fig.3J.xlsx : Comparison of the bending angles of biohybrid unit actuators. ### Fig. 4: Serially-arranged biohybrid unit actuators. * File Fig.4D.xlsx: Whole bending angle of the serially-arranged biohybrid actuator with different electric field intensities. - File Fig.4E.xlsx: Comparison of the actuator’s whole bending angle with different electric field intensities. - File Fig.4F.xlsx: The bending angle of each joint with different electric field intensities. ### Fig. 6: Formation and evaluation of the antagonistic biohybrid unit actuators. * File Fig.6E.xlsx: Relationship between the duration of the applied electric field and the bending angle of the actuator. The vertical axis represents the average angle rotated to the left and right. - File Fig.6F.xlsx: Relationship between the electrode-muscle distance *d* and the average rotational angle (duration of electric field application was 750 ms). * File Fig.6G.xlsx: Measurement results of contractile force in relation to the number of muscle rings stacked on one pair of anchors. - File Fig.6H(c).xlsx: The difference in average rotational angles with or without the shielding structure. ### Fig. 7: Slither-type multi-joint biohybrid robot.  * Fig. 7D_All joint angle.xlsx : Time-lapse of the strain of each muscle ring stack under the selective sequential stimulation. - File Fig.7G_Xdisp.xlsx: Time course of the displacement of the slither-type multi-joint robot's tip in X direction. - File Fig.7G_Ydisp.xlsx: Time course of the displacement of the slither-type multi-joint robot's tip in Y direction. ### Supplementary Figures: * file S1B.xlsx : Relationship of the groove widths and the width of the constructed muscle rings. * file S1C(b).xlsx : Measured width at each circumferential point number. * file S1C(c).xlsx : The ratio of the maximum to minimum width of the muscle ring (tmax/tmin). * file S3_cell density.pdf：Designated areas (white circular lines) within the cross-section of the muscle ring for cell counting. The cell density was calculated by dividing average cell numbers by cross-sectional area of designated area (0.041 mm^2). * file S3B.xlsx : Fluorescence intensity of red (α-actinin) from the start point to the end point of the line drawn in the cross-sectional images. * file S3C.xlsx : Density of cell nuclei within cross-sections of the muscle rings. * file S5B.xlsx : Changes in the bending angle of the substrate (θ’-θ) with muscle ring contraction over the culture days. * file S6B, S6C, S6D, S6E.xlsx : Deflection amounts and deflection angles of the muscle strip and muscle rings. * file S11.xlsx : Transition of the contractile force of the muscle ring over culture days. * file S12.xlsx : The relationship between the width of the muscle rings and the contractioninduced circumferential change rate * file S13.xlsx : Locomotion analysis of the slither-type multi-joint biohybrid robot with reduced bottom surface friction. * file S14.xlsx : Calibration of the force sensor. ### Units and abbreviations : #### **In all files:** * deg: degree * n: number of samples * s: second * g: gram * V: voltage * MPC : 2-methacryloyloxyethyl phosphorylcholine * PDMS: polydimethylsiloxane  * ECM: extracellular matrix **In file 2B.xlsx:**   * culture day: days since the start of muscle ring culture [-] * width of the muscle ring: the width of muscle ring tissues measured by observing from the bottom using confocal microscopy [mm] **In file 2C.xlsx:**  * tracking point (P): The reference point defined in the image analysis software for measuring displacement * radial contraction displacement of the reference point:  The displacement of the reference point upon muscle contraction, measured as the distance between the center of the muscle ring and the reference point [µm] * time [s]: time [second]  **In file 2D.xlsx:** * n: number of muscle ring * strain: changes in circumferences of muscle rings by applying tensile force from anchors [%] * Vbefore, Vafter: detected values of voltage before and after muscle contraction [V] * Vpp: peak-to-peak value of voltage (Vafter-Vbefore) [V] * contractile force: The value obtained by multiplying Vpp by the sensitivity coefficient 10.8 [mN] * passive force: The value obtained by multiplying the voltage corresponding to the passive tension of the muscle ring  by the sensitivity coefficient 10.8 [mN]  **In file 2G.xlsx:** * grooves: grooves made within culture substrates to form muscle rings * PDMS stiffness: The stiffness, of the pillar-shaped supporter calculated using the cantilever beam deflection formula as follows: k = 3 ∙ E ∙ I / (L^3) [N/mm] * force: contractile force [mN] * number: number of muscle ring * pillar-shaped supporter: central pillar structure formed in the culture substrate **In file 2I.xlsx:** * external tensile strain: change in the circumference of the muscle rings when stretched between anchors * ECM4.3µL, ECM8.7µL, ECM13µL, ECM17µL: Amount of extracellular matrix used in muscle ring culture per one sample [µL] **In file 2J.xlsx:** * time: time [second] * n: number of muscle ring * force: contractile force [mN] **In file 2K.xlsx:** * cells/ml: cell density * cells: total cell number * tissue: muscle ring **In file 2L.xlsx:** * Hz:  electric field intensity **In file 2M.xlsx:** * Vpassive: (voltage after extension of muscle rings) - (voltage without extension) [Voltage] * Vactive: (voltage after contraction of muscle rings) - (voltage after extension of muscle rings) [Voltage] * average: average of contractile forces (sum of contractile forces /number of samples) [mN] **In file 2N.xlsx:** * Vtop: voltage detected by force sensor after muscle contraction [Voltage] * Vbottom: voltage detected by force sensor before muscle contraction [Voltage] **In file 3C.xlsx:** * P, P': tracking point before (P) and after (P') actuation  * Displacement (Z direction):  Distance between the point P' and P [mm] **In file 3E.xlsx:** * strip: muslce strip  * ring: muscle ring **In file 3F.xlsx:** * substrate bending angle: [degree] **In file 3G.xlsx:** * muscle ring, hooked: unit actuator powered by a muscle ring hooked onto C-shaped anchors * muscle strip, fixed: unit actuator powered by a muscle strip pre-fixed by C-shaped anchors **In file 3I, 3J.xlsx:** * ring, fibronectin-coated: unit actuator assembled by a muscle ring and fibronectin-coated anchors * ring, non-coated: unit actuator assembled by a muscle ring and non-coated anchors * ring, mpc-coated: unit actuator assembled by a muscle ring and mpc polymer-coated anchors **In file 4D, 4E.xlsx:** * fixed: biohybrid unit actuators powered by muscle strips * hooked: biohybrid unit actuators powered by muscle rings * whole bending angle: angle formed by the line connecting the actuator's tip and base before and after actuation [degree] **In file 4E.xlsx:** * 1, 2, 3: number of the serially-arranged biohybrid unit actuator **In file 4F.xlsx:** * 1st, 2nd, 3rd joint:  **In file 6E.xlsx:** * Duration time of electric field application [milli-second] * frequency: electric frequency [Hz] * θleft, θright: left and right rotational angle of the antagonistic unit actuators [degree] * average rotational angle: (*θleft* + *θright*) / 2 [degree] **In file 6F.xlsx:** * Distance between the electrode [mm] **In file 6G.xlsx:** * 1 muscle ring, 2 muscle rings, 3 muscle rings, 4 muscle rings: number of stacked muscle rings onto one pair C-shaped anchor structures **In file 6H(c).xlsx:** * presense, absense: presense or absense of the shielding structure incorporated into the slither-type biohybrid robots * d: distance between the electrode and the muscle rings [mm] **In file 7D_All joint angle.xlsx:** * Joint_Upper, Joint_Lower: The upper and lower sides of each joint captured in the state shown in Fig. 7D **In file 7G_Xdisp, 7G_Ydisp.xlsx:** * disp: displacement of tracking point from start position [mm] * displacement (X): displacement in x direction [mm] * displacement (Y): displacement in y direction [mm] **In file S1B.xlsx:** * groove dimension: height and width of grooves (h×w) formed within culture substrates [mm×mm] **In file S1C(b).xlsx:** * w: width of muscle ring [mm] **In file S1C(c).xlsx:** * groove width: the width of each groove [mm] * average: (total measured widths) / (number of samples) [mm] * tmax/tmin: ratio between the maximum and minimum widths of each muscle ring [mm] **In file S3B.xlsx:** * fluorescent intensity : red intensity measured by ImageJ, scaled between 0 (min) and 255 (max) [-] * distance : the distance from the top end along a vertical line drawn from the top to the bottom of the image center [mm] **In file S3C.xlsx:** * /mm^2 : (number of cell nuclei [-]) / (cross-sectional area of muscle ring within the counted area [mm^2]) **In file S5B.xlsx:** * t : the thickness of the substrate at its thinnest point [µm] **In file S6B, S6C, S6D, S6E.xlsx:** * sample: the unit actuator **In file S11.xlsx:** * culture days: number of days since the start of muscle ring culture **In file S12.xlsx:** * contraction-induced circumferential change rate:  * ring, hooked (MPC):  **In file S13.xlsx:** * displacement: displacement of tracking point from start position [mm] **In file S14.xlsx:** * specification data: Calibration curve data provided by THK Precision Corp.