Deridoux A et al. (2026), Tube feet dynamics drive adaptation in sea star...

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Proc Natl Acad Sci U S A 2026 Jan 20;1233:e2509681123. doi: 10.1073/pnas.2509681123.

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Tube feet dynamics drive adaptation in sea star locomotion.

Deridoux A, Heydari S, Gorb SN, Kanso E, Flammang P, Gabriele S.

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Sea stars use hundreds of tube feet on their oral surface to crawl, climb, and navigate complex environments, despite lacking a central brain. While tube foot morphology and function as muscular hydrostats are well described, the mechanisms that coordinate their collective dynamics remain poorly understood. To investigate these dynamics, we employed an optical imaging method based on frustrated total internal reflection (FTIR) to visualize and quantify tube foot adhesive contacts in real time in the species Asterias rubens across individuals spanning a wide size range. Our results reveal an inverse relationship between crawling speed and tube foot adhesion time, indicating that sea stars regulate locomotion by modulating contact duration in response to mechanical load. To test this, we conducted perturbation experiments using 3D-printed backpacks that increased body mass by 25 and 50%, along with biomechanical modeling of decentralized feedback control of the tube feet. The added load significantly increased adhesion time, supporting the role of a load-dependent mechanical adaptation. We further investigated inverted locomotion, both experimentally and through simulation, and found that tube feet adjust their contact behavior when the animal is oriented upside down relative to gravity. Together, these findings demonstrate that sea stars adapt their locomotion to changing mechanical demands by modulating tube foot-substrate interactions, revealing a robust decentralized control strategy in a brainless organism and highlighting general principles of distributed control in biology and soft robotics.

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	Fig. 1. Allometric scaling in sea stars. (A) Relationship between the average arm length and the sea star mass across 8 species with five arms: Asterina gibbosa (red, n = 37), Echinaster sepositus (green, n = 14), Asterias rubens (orange, n = 74), Marthasterias glacialis (blue, n = 23), Linckia laevigata (light blue, n = 2), Patiria miniata (purple, n = 4), Dermasterias imbricata (black, n = 2), and Pentaceraster mammillatus (pink, n = 1). Each dot represents one individual (n = 157 sea stars, R2 = 0.9541, P < 0.0001). The estimated slope is 0.41 (95 % CI 0.40 to 0.43), indicating positive allometry between arm length and body mass. (B) Oral and lateral views of two individuals of A. rubens illustrating size variability. (C) Range of sizes observed in A. rubens. (Scale bar, 50 mm.) (D) Relationship between the body mass and the average arm length (n = 74, R2 = 0.7629, P < 0.0001). (E) Relationship between the average tube feet number per arm and the average arm length of A. rubens individuals (n = 40, R2 = 0.7056, P < 0.0001). (F) Aboral view of A. rubens showing labeled arms and the corresponding interarm angles. (Scale bar, 25 mm.) (G) Measurements of interarm angle (n = 29). All data are color-coded by individual mass with *P < 0.05 and ns is not significant.
	Fig. 2. Quantification of tube feet dynamics using FTIR-based imaging. (A) Schematic representation of the experimental setup, which adapts the principle of FTIR to a custom-designed aquarium. When tube feet make contact with the FTIR-equipped glass surface, they disrupt the total internal reflection, causing light to scatter and locally illuminate the contact area. Sea stars are allowed to move freely, and their movements are recorded from below using a camera positioned beneath the tank. (B) Photograph of the experimental setup showing the aquarium equipped with an FTIR-based imaging system. The inset provides a close-up view of an A. rubens arm, where contact points of individual tube feet with the substrate are clearly visible during locomotion (arrow). (C) Image of the oral surface of A. rubens crawling within the experimental setup. (D) Image analysis pipeline developed to quantify the number of adhering tube feet and their contact area over time from image sequences. The method includes contrast enhancement, thresholding, and automated detection for accurate temporal tracking.
	Fig. 3. Crawling speed in A. rubens is not affected by the number of adhering tube feet. (A) Displacement of A. rubens recorded over 20 s, with the number of tube feet in contact and the contact area measured every 0.2 s. (B) Average number of tube feet in contact over time for individuals of increasing mass (color-coded from light to dark: 11.39 g, 20.96 g, 37.75 g, and 68.31 g). (C) Relationship between the average number of tube feet in contact and body mass (n = 39, R2 = 0.3536, P < 0.0001). (D) Crawling speed as a function of the average number of tube feet in contact and body mass (n = 39). (E) Relationship between the percentage of tube feet in contact and body mass (n = 39, R2 = 0.0926, P = 0.0002). (F) Relationship between the crawling speed and the average percentage of tube feet in contact (n = 39). All data are presented as mean ± SD.
	Fig. 4. Tube foot adhesion time correlates with sea star locomotion in A. rubens. (A) High-magnification imaging reveals the three stages of tube foot adhesion during locomotion. Top panels show side views of an individual in motion, while Bottom panels display views of the ambulacral groove. Adhesion time is defined as the duration of the adhesion stage. (B) Temporal variation in the circularity index of individual tube feet (n = 10). Vertical lines indicate the start and end of the adhesion phase. (C) Relationship between mean tube foot contact area and body mass (n = 39, R2 = 0.6203, P < 0.0001). In log–log space, the slope is 0.42 (95 % CI 0.38 to 0.47), showing that contact area increases more slowly than predicted by isometry, consistent with negative allometry. (D) Relationship between mean adhesion time and tube foot contact area (n = 39, R2 = 0.3088, P < 0.0001). (E) Crawling speed as a function of tube foot adhesion time (n = 49, R2 = 0.2115, P < 0.0001). All data are presented as mean ± SD.
	Fig. 5. Sea star locomotion dynamics in response to load changes are modulated by adhesion time in A. rubens. (A) Photographs showing two representative sizes of 3D-printed backpacks used to artificially increase the body mass by 25 and 50% with stainless steel beads. (B) Percentage of tube feet in contact with the substrate, (C) instantaneous crawling speed, and (D) tube foot adhesion time under four conditions: normal locomotion, empty backpack, +25% body mass, and +50% body mass (N = 5 sea stars per condition). Data in all superplots are color-coded by mass. Each small dot corresponds to a single tube foot contact event, and large dots indicate means per individual. Three replicates were performed per sea star. (E) Schematic of the biomechanical model used to simulate sea star locomotion through locally controlled tube feet. (1) Model organism propelled by 10 tube feet. The inset defines key parameters: tube foot length (l), tilt angle (θ), and interfoot spacing (d). (2) Mechanical model of a single tube foot, composed of a passive linear spring and an active force generator capable of producing either pushing or pulling forces depending on muscle activation. (3) Active force profile based on Hill’s muscle model. (4) Local control policies at the level of individual tube feet. These define the probability of transitions between pushing and pulling states and between attached and detached states, based on sensory feedback. (5) Tube feet detach when stretched beyond a threshold length ldetach. (F) The corresponding length of detachment for the tube feet are ldetach = 0.9, 0.95, 1, respectively. Parameter values are N =100, L = 40, l = 1, Fmax = 0.4, λ = 5 (G) Simulated crawling speed and (H) attachment fraction τ, with τ=∑i=1NTiattached/NT, defined as the sum over all tube feet of the time Tiattached each foot spends in attachment, divided by the total simulation time T times the number N of tube feet. Both metrics are shown as a function of sea star mass, increasing from baseline to highest (W = 2, 2.5, 3). For each mass condition, 25 simulations were performed with randomized initial foot states. *P < 0.001, **P < 0.0001, and ns = not significant.
	Fig. 6. Modulation of adhesion time enables A. rubens to adapt its locomotion under inverted conditions. (A) Schematic of the experimental setup for inverted locomotion. Sea stars were allowed to crawl upside down, while their oral surface was recorded from above using a camera positioned over the aquarium. (B) Percentage of tube feet in contact, (C) instantaneous crawling speed, and (D) tube foot adhesion time for normal versus inverted conditions (N = 6 sea stars per condition). All data are displayed as superplots, showing individual data points. Each dot corresponds to an individual contact event, and large dots indicate means per individual. Each individual was tested in three replicates. (E) Simulated crawling speed and (F) attachment fraction τ=∑i=1NTiattached/NT, defined as the sum over all tube feet of the time Tiattached each foot spends in attachment, divided by the total simulation time T times the number N of tube feet. Both shown for the flat and inverted sea stars. For each orientation, 25 random simulations have been performed. Parameter values are N=100,L=40,l=1,Fmax=0.4,λ=5, with no parameter adjustment between normal and inverted simulations. ****P < 0.0001.
	Fig. 1. Allometric scaling in sea stars. (A) Relationship between the average arm length and the sea star mass across 8 species with five arms: Asterina gibbosa (red, n = 37), Echinaster sepositus (green, n = 14), Asterias rubens (orange, n = 74), Marthasterias glacialis (blue, n = 23), Linckia laevigata (light blue, n = 2), Patiria miniata (purple, n = 4), Dermasterias imbricata (black, n = 2), and Pentaceraster mammillatus (pink, n = 1). Each dot represents one individual (n = 157 sea stars, R2 = 0.9541, P < 0.0001). The estimated slope is 0.41 (95 % CI 0.40 to 0.43), indicating positive allometry between arm length and body mass. (B) Oral and lateral views of two individuals of A. rubens illustrating size variability. (C) Range of sizes observed in A. rubens. (Scale bar, 50 mm.) (D) Relationship between the body mass and the average arm length (n = 74, R2 = 0.7629, P < 0.0001). (E) Relationship between the average tube feet number per arm and the average arm length of A. rubens individuals (n = 40, R2 = 0.7056, P < 0.0001). (F) Aboral view of A. rubens showing labeled arms and the corresponding interarm angles. (Scale bar, 25 mm.) (G) Measurements of interarm angle (n = 29). All data are color-coded by individual mass with *P < 0.05 and ns is not significant.
	Fig. 2. Quantification of tube feet dynamics using FTIR-based imaging. (A) Schematic representation of the experimental setup, which adapts the principle of FTIR to a custom-designed aquarium. When tube feet make contact with the FTIR-equipped glass surface, they disrupt the total internal reflection, causing light to scatter and locally illuminate the contact area. Sea stars are allowed to move freely, and their movements are recorded from below using a camera positioned beneath the tank. (B) Photograph of the experimental setup showing the aquarium equipped with an FTIR-based imaging system. The inset provides a close-up view of an A. rubens arm, where contact points of individual tube feet with the substrate are clearly visible during locomotion (arrow). (C) Image of the oral surface of A. rubens crawling within the experimental setup. (D) Image analysis pipeline developed to quantify the number of adhering tube feet and their contact area over time from image sequences. The method includes contrast enhancement, thresholding, and automated detection for accurate temporal tracking.
	Fig. 3. Crawling speed in A. rubens is not affected by the number of adhering tube feet. (A) Displacement of A. rubens recorded over 20 s, with the number of tube feet in contact and the contact area measured every 0.2 s. (B) Average number of tube feet in contact over time for individuals of increasing mass (color-coded from light to dark: 11.39 g, 20.96 g, 37.75 g, and 68.31 g). (C) Relationship between the average number of tube feet in contact and body mass (n = 39, R2 = 0.3536, P < 0.0001). (D) Crawling speed as a function of the average number of tube feet in contact and body mass (n = 39). (E) Relationship between the percentage of tube feet in contact and body mass (n = 39, R2 = 0.0926, P = 0.0002). (F) Relationship between the crawling speed and the average percentage of tube feet in contact (n = 39). All data are presented as mean ± SD.
	Fig. 4. Tube foot adhesion time correlates with sea star locomotion in A. rubens. (A) High-magnification imaging reveals the three stages of tube foot adhesion during locomotion. Top panels show side views of an individual in motion, while Bottom panels display views of the ambulacral groove. Adhesion time is defined as the duration of the adhesion stage. (B) Temporal variation in the circularity index of individual tube feet (n = 10). Vertical lines indicate the start and end of the adhesion phase. (C) Relationship between mean tube foot contact area and body mass (n = 39, R2 = 0.6203, P < 0.0001). In log–log space, the slope is 0.42 (95 % CI 0.38 to 0.47), showing that contact area increases more slowly than predicted by isometry, consistent with negative allometry. (D) Relationship between mean adhesion time and tube foot contact area (n = 39, R2 = 0.3088, P < 0.0001). (E) Crawling speed as a function of tube foot adhesion time (n = 49, R2 = 0.2115, P < 0.0001). All data are presented as mean ± SD.
	Fig. 5. Sea star locomotion dynamics in response to load changes are modulated by adhesion time in A. rubens. (A) Photographs showing two representative sizes of 3D-printed backpacks used to artificially increase the body mass by 25 and 50% with stainless steel beads. (B) Percentage of tube feet in contact with the substrate, (C) instantaneous crawling speed, and (D) tube foot adhesion time under four conditions: normal locomotion, empty backpack, +25% body mass, and +50% body mass (N = 5 sea stars per condition). Data in all superplots are color-coded by mass. Each small dot corresponds to a single tube foot contact event, and large dots indicate means per individual. Three replicates were performed per sea star. (E) Schematic of the biomechanical model used to simulate sea star locomotion through locally controlled tube feet. (1) Model organism propelled by 10 tube feet. The inset defines key parameters: tube foot length (l), tilt angle (θ), and interfoot spacing (d). (2) Mechanical model of a single tube foot, composed of a passive linear spring and an active force generator capable of producing either pushing or pulling forces depending on muscle activation. (3) Active force profile based on Hill’s muscle model. (4) Local control policies at the level of individual tube feet. These define the probability of transitions between pushing and pulling states and between attached and detached states, based on sensory feedback. (5) Tube feet detach when stretched beyond a threshold length ldetach. (F) The corresponding length of detachment for the tube feet are ldetach = 0.9, 0.95, 1, respectively. Parameter values are N =100, L = 40, l = 1, Fmax = 0.4, λ = 5 (G) Simulated crawling speed and (H) attachment fraction τ, with τ=∑i=1NTiattached/NT, defined as the sum over all tube feet of the time Tiattached each foot spends in attachment, divided by the total simulation time T times the number N of tube feet. Both metrics are shown as a function of sea star mass, increasing from baseline to highest (W = 2, 2.5, 3). For each mass condition, 25 simulations were performed with randomized initial foot states. *P < 0.001, **P < 0.0001, and ns = not significant.
	Fig. 6. Modulation of adhesion time enables A. rubens to adapt its locomotion under inverted conditions. (A) Schematic of the experimental setup for inverted locomotion. Sea stars were allowed to crawl upside down, while their oral surface was recorded from above using a camera positioned over the aquarium. (B) Percentage of tube feet in contact, (C) instantaneous crawling speed, and (D) tube foot adhesion time for normal versus inverted conditions (N = 6 sea stars per condition). All data are displayed as superplots, showing individual data points. Each dot corresponds to an individual contact event, and large dots indicate means per individual. Each individual was tested in three replicates. (E) Simulated crawling speed and (F) attachment fraction τ=∑i=1NTiattached/NT, defined as the sum over all tube feet of the time Tiattached each foot spends in attachment, divided by the total simulation time T times the number N of tube feet. Both shown for the flat and inverted sea stars. For each orientation, 25 random simulations have been performed. Parameter values are N=100,L=40,l=1,Fmax=0.4,λ=5, with no parameter adjustment between normal and inverted simulations. ****P < 0.0001.