Abstract
Snakes exhibit a wide variety of gaits, including gliding in air and sidewinding on land, which is particularly notable for its out-of-plane motion. Here we report the observation of another non-planar gait used as an escape strategy from threatening situations by juvenile anacondas (Eunectes notaeus), which we refer to as the S-start due to its shape. In this transient mode of locomotion, the snake writhes and bends out of the plane while rolling forward about its midsection without slippage. To quantify our observations, we develop a model for an active non-planar filament that interacts anisotropically with a frictional substrate. We demonstrate that locomotion is due to a propagating localized pulse of a topological quantity—the link density. A two-dimensional phase space characterized by scaled body weight and muscular torque shows that relatively light juveniles are capable of S-starts, whereas heavy adults are not, consistent with our experiments. We also show that a periodic sequence of S-starts naturally leads to a sidewinding gait.
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Data availability
The data that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.
Code availability
Code used for the simulation is available via GitHub at https://github.com/Chelakkot/S-start.
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Acknowledgements
We thank NSF grants BioMatter DMR 1922321, MRSEC DMR 2011754 and EFRI 1830901, the Simons Foundation and the Henri Seydoux Fund (L.M.) for partial financial support.
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Contributions
B.Y. observed the escape behaviour and carried out the experiments with snakes. L.M. conceived and designed the study and approaches. N.C. performed the numerical simulations, in consultation with R.C., M.G. and L.M. L.M. conceived of the mathematical model, the phase space and the scaling laws. N.C., R.C. and L.M. wrote the paper. L.M. supervised the study.
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Supplementary information
Supplementary Information
Supplementary Sections I–VII (describing the experimental methods, mathematical model and simulation parameters), Figs. 1–5, Tables I–III and refs. 1–11.
Supplementary Video 1
Experimental observations of S-start in baby yellow anacondas: we show the top-down and side-on views, slowed down by a factor of 25×. In real time, one cycle of the S-start takes approximately 0.5 s.
Supplementary Video 2
Simulations of the S-start and friction-dominated and inertia-dominated snake gaits: these correspond to the phases depicted in Fig. 3b. The red snake surface indicates contact with the ground, whereas yellow indicates a lifted portion of the snake body. Snake contact with the ground is marked by a grey trace left on the ground, showing that the central contact point traces an approximately straight path. Simulation parameters are listed in Supplementary Tables II and III, except that we use length L = 1.4 m and maintain diameter a = 0.04 m. We increased the length of this video to prolong the S-start process to allow for better visualization. All the parameters except lifting torque and mass density remain constant between simulations of the three locomotion modes. Lifting torque for friction-dominated motion corresponds to Γ = 6.3 × 103 Pa; for the S-start, lifting corresponds to Γ = 9.4 × 104 Pa, and for inertia-dominated, to Γ = 1.9 × 104 Pa. Mass density for friction-dominated motion corresponds to ρ = 800 kg m–3; for the S-start, ρ = 460 kg m–3; and for inertia-dominated motion, ρ = 80 kg m–3. Note that the values used for Γ and ρ in each type of locomotion are within an order of magnitude of what would be expected experimentally based on the results of Supplementary ref. (10). We vary them from this expected value to produce different forms of locomotion. Note that it is the dimensionless ratio \(R=\frac{{\rho} {g}\,{L}^{2}}{{\varGamma} {a}}\) that determines the type of locomotion (Fig. 3a). Computing this ratio for each simulation shown in this video, we get Rfriction = 61, RS = 23 and Rinertia = 20. As expected, Rfriction < RS < Rinertia. Note that Rinertia falls in the lower half of the S-start regime (Fig. 3a) rather than in the inertia-dominated regime; this may be due to the fact that a/L is smaller here than in the simulations used for Fig. 3a.
Supplementary Video 3
Experimental and simulated sidewinding motion: experiments are obtained from ref. 12, which can be found at https://science.sciencemag.org/content/suppl/2014/10/08/346.6206.224.DC1. Simulation procedures are described in Supplementary Section V. As shown in Supplementary Video 2, the red snake surface indicates contact with the ground, whereas yellow indicates a lifted region. Contact with ground is marked by a grey trace left on the ground, showing the parallel straight paths traced by the contact points of successive torque wave triplets. The simulation settings are described in Supplementary Tables II and III. For comparison to the S-start, the dimensionless ratio R = ρgL2/Γa is Rsidewinding = 16.7.
Supplementary Video 4
Experimental observation of S-start in baby anaconda in real time: we show the top-down view of S-start in real time.
Source data
Source Data Fig. 1
Unprocessed, compressed image files used in Fig. 1.
Source Data Fig. 2
Compressed data files for Fig. 2.
Source Data Fig. 3
Compressed data files for Fig. 3.
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Charles, N., Chelakkot, R., Gazzola, M. et al. Topological dynamics of rapid non-planar gaits in slithering snakes. Nat. Phys. 21, 856–860 (2025). https://doi.org/10.1038/s41567-025-02835-7
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DOI: https://doi.org/10.1038/s41567-025-02835-7
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