Context-dependent mechanical reconfiguration is necessary for multifunctional behavior in a constrained hydrostat

Muscular hydrostats, muscular structures with no rigid skeleton, are ubiquitous within the animal kingdom, from vertebrate tongues to cephalopod arms1,2, but how they perform complex actions remains poorly understood. One model hydrostat studied for its neural control3-7 and biomechanics8-17 is the feeding system (buccal mass) of the sea hare Aplysia (Fig. 1). The buccal mass (Fig. 1b) performs multiple feeding behaviors by coordinating intrinsic muscles to move a grasper (odontophore)18,19. In this paper, we investigated how mechanical reconfiguration from interacting shape-changing elements facilitates large odontophore protractions. During rejection behaviors, mechanical reconfiguration of the odontophore (elongating its shape to a higher aspect ratio) stretches a protractor muscle (I2), allowing I2 to generate stronger protractions12. In biting behaviors, the odontophore has a similar range of motion. However, during biting, the odontophore has a lower aspect ratio throughout protraction, meaning the I2 muscle alone is insufficient to reach observed protractions due to its length/tension property and reduced mechanical advantage9,10,12,18. By combining new analysis of MRI movies of Aplysia feeding12,18 (Fig. 1) with a new biomechanical model for biting and rejection (Fig. 2), we demonstrate two context-dependent mechanical reconfiguration mechanisms that explain the different ways large protractions are produced in biting and rejection (Fig. 3). The mechanisms integrate shape changes, bending and conforming of muscle structures, and shifts in contact interactions. We propose two mechanical subclasses of muscular hydrostats, "constrained" or "unconstrained" (Fig. 4), that may be morphologically similar but employ different control strategies depending on whether mechanical constraints are reliably present. O_FIG O_LINKSMALLFIG WIDTH=150 HEIGHT=200 SRC="FIGDIR/small/715937v1_fig1.gif" ALT="Figure 1"> View larger version (87K): org.highwire.dtl.DTLVardef@1c60cbeorg.highwire.dtl.DTLVardef@16ebd04org.highwire.dtl.DTLVardef@13b65d5org.highwire.dtl.DTLVardef@9aafb0_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFig. 1.C_FLOATNO Anatomy and kinematics of the Aplysia feeding system (a1) Adult Aplysia californica searching for food and (a2) feeding on Gracilaria macroalgae ((a1) photo credit: Dr. Jeffrey P. Gill, (a2) modified with permission from Bennington et al. 202514). Gray highlight shows the location of the feeding structure, the buccal mass (b). (b) An anatomical diagram of a midline sagittal view of a buccal mass. During feeding, the odontophore (the internal grasper of the buccal mass) protracts through the tubelike I3 muscle. In the midsagittal plane, the I3 is visible as two longitudinal elements, but is one continuous structure that runs circumferentially around the buccal mass. The inner wall of the distal I3 is shown in dark blue. The dashed white line shows the jaw line, which is used as the reference for both the translation and rotation measurements. (c) Configuration of the buccal mass (left: anatomical diagram; middle: MRI frames) showing (c1) peak retraction and (c2) peak protraction. (right) A diagram of the buccal mass was created to highlight key anatomical landmarks for each frame of the MRI video showing a complete biting sequence (d-e). The same diagrammatic representations of the landmarks are shown in (d) and (e) for the protraction and retraction portions of the biting sequence, respectively (See STAR Methods). The frames shown in (c1) and (c2) correspond to the 0 ms and 3410 ms frames, respectively, and are the same between the middle and right portions of the figure. Key frames referred to in the text: t0: start of the behavioral cycle, t1: peak rotation reached, t2: peak translation reached, t3: rotation plateau ended, t4: end of behavioral cycle. (f) Kinematic measurements were taken using the drawn diagrams for each frame in the sequence. See main text for definitions of variables. All scale bars correspond to 10 mm. C_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=84 SRC="FIGDIR/small/715937v1_fig2.gif" ALT="Figure 2"> View larger version (34K): org.highwire.dtl.DTLVardef@1848bb9org.highwire.dtl.DTLVardef@f126a4org.highwire.dtl.DTLVardef@1ffd5forg.highwire.dtl.DTLVardef@336910_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFig. 2.C_FLOATNO Kinetic/Kinematic biomechanical model of the buccal mass (a) Rest geometry of the biomechanical model. The grasper (odontophore) is modeled as a rigid ellipse (magenta with yellow radula). It is connected to the I1/I3 lumen (blue trapezoid) by the hinge muscle (green). The I2 protractor muscle (red) wraps conformally around the odontophore and attaches at the lateral groove. The net force and torque from the I2 on the odontophore are found by performing an instantaneous force balance on a small arc of the ellipse and integrating across the full region of contact between the I2 and the odontophore. The hinge muscle is modeled as a linearly elastic, geometrically exact beam. At each position along the beams midline, a quasistatic force balance is performed (see STAR Methods). (b1) The tension in the I2 is modeled using the length-tension relationship reported in Yu et al. 1999 scaled by a normalized activation level. (b2) The axial and bending stiffness of the beam hinge were calibrated to ex vivo animal data reported in Sutton et al. 2004. Gray region indicates odontophore displacements observed during biting behaviors (Sutton et al. 2004). (c1-c2) To investigate the effects of mechanical reconfiguration on odontophore position at peak protraction, (c1) the aspect ratio of the odontophore ellipse and (c2) the stretch of the lateral groove were added as additional kinematic constraints. (c1) and (c2) show results from the model but do not correspond to any particular behavior or configuration observed in the animal. These constraints impact the biomechanical model via contact forces from the I1/I3 (see STAR Methods). The lateral groove stretch is converted to a depression angle of the dorsal I1/I3 muscle as a proxy for the wrapping of the dorsal I3 around the odontophore observed during in vivo feeding behaviors (Fig 1). (d-e) MRI frames at peak protraction in (d1, with and without overlay) biting (t2) and (e1, with and without overlay) rejection ({tau}2) compared to corresponding frames from the biomechanical model (d2 and e2, respectively). C_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=184 SRC="FIGDIR/small/715937v1_fig3.gif" ALT="Figure 3"> View larger version (56K): org.highwire.dtl.DTLVardef@1369a90org.highwire.dtl.DTLVardef@1dda429org.highwire.dtl.DTLVardef@4485d5org.highwire.dtl.DTLVardef@ae6523_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFig. 3.C_FLOATNO Mechanical reconfiguration of the buccal mass (a) Midsagittal kinematics of the buccal mass during a (left) biting and (right) rejection behavior (see also Figs. S1 and S2). Colored circles (diamonds) show data for an individual frame, and the black line shows the two-point moving average of the signal. Vertical dashed lines show concurrent time points in the different kinematic signals (biting: t0: cycle starts, t1: peak rotation, t2: peak translation, t3: rotation plateau ended, t4: cycle ends. Rejection: {tau}0: cycle starts, {tau}1: rotation plateau ends, {tau}2: peak translation, {tau}3: peak rotation, {tau}4: cycle ends). (b) Model configurations for nine different pairs of aspect ratios ({Phi}) and lateral groove stretches ({lambda}LG ) (numbers correspond to the labeled points in (Fig. S6c)). Note that these simulated results from the model do not necessarily correspond to configurations observed in the animal but rather show changes in the systems configuration due to changes in the kinematic parameters. All configurations here were achieved with an I2 activation of AI2 = 65%. (c-d) Sensitivity of the model translation and rotation at peak protraction to lateral groove shortening ({lambda}LG, top row) and aspect ratio change ({Phi}, bottom row) for biting (c) and rejection (d). The y-axis for all panels reports the difference between the model prediction and observed animal value at peak protraction (for translation or rotation) normalized by the range of motion (ROM) for each behavior. For each panel, one kinematic parameter is held fixed (top:{Phi} fixed; bottom:{lambda} LG fixed) at the value observed in the animal at peak protraction, and the other is varied to determine the effect of changing this parameter on the translation and rotation of the odontophore. Vertical dashed lines show the observed value of the varied parameter in the animal at peak protraction. The horizontal dashed line shows 0 difference for reference. The steepness of the difference curve in the vicinity of the vertical dashed line indicates how sensitive the system is to changes in each kinematic parameter near peak protraction. Here, a steeper curve (with a positive or negative slope) indicates greater sensitivity. For biting simulations, AI2 = 15%, and for rejection, AI2 = 90% based on the results of the model validation. Each curve in (c) and (d) is a 1D cross-section of the 2D contour plots shown in Figs. S6-S7. For a complete view of the sensitivity of translation and rotation to lateral groove stretch and aspect ratio across the kinematic configuration space at different I2 activations, see Figs. S6-S7. Note that (c) and (d) use different vertical scales. The smaller scale for the rejection plots was chosen to better show the difference curves for rejection, and it reflects the overall decreased sensitivity to both lateral groove stretch and aspect ratio changes for the rejection behaviors. C_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=111 SRC="FIGDIR/small/715937v1_fig4.gif" ALT="Figure 4"> View larger version (36K): org.highwire.dtl.DTLVardef@171f4c6org.highwire.dtl.DTLVardef@7d11a7org.highwire.dtl.DTLVardef@11206e3org.highwire.dtl.DTLVardef@82489c_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFig. 4.C_FLOATNO Mechanical reconfiguration facilitates behaviors in a variety of constrained hydrostat systems Combinations of the active shape change of internal structures (cyan), changes to the movement constraints and contact interaction (blue), and bending and conforming of structures (magenta) allow constrained hydrostats to mechanically reconfigure their neuromusculature (purple) to perform various behaviors. This can be seen in various systems across various species. As discussed here, the Aplysia buccal mass uses combinations of these mechanisms in (a) biting and (b) rejection behaviors to protract the buccal mass. (c) The pond snail, Lymnaea, has a morphologically similar buccal mass to Aplysia, but its I1/I3 homolog, the anterior jugalis, sits further posterior to the odontophore35, meaning it may more readily rely on the bending of the anterior jugalis and contact interactions during protraction. (d) The octopus and, more broadly, cephalopod buccal masses contain a beak that lacks a fixed articulation. Instead, by activating the lateral mandibular muscle (LMM), the buccal mass can create a stiff rotation point and may shift the function of the posterior mandibular muscle (PMM) from compressing the buccal mass to opening the beak36,37. (e) The human tongue (and other Type I tongues38) sits within the skull and makes use of contact with the hard palate to push food from the oral cavity into the pharynx27,48. (f) Additionally, by changing how the tongue interacts with the palate and teeth, while maintaining the same internal shape, humans can produce various vowel and consonant sounds39,49,50. This use of contact with the palate and teeth is known in the phonetics community as "bracing." Here, by creating a groove in the middle of the tongue, the phonemes /{varepsilon}/ and /ae/ can be produced. By raising the tongue and creating palatal contact while maintaining that groove, these vowels shift to the fricative consonants /s/ and /{theta}/49. Small insets show which of the mechanical configurations are used in each behavior. C_FIG