1. Computational and Systems Biology
  2. Neuroscience
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Integrative neuromechanics of crawling in D. melanogaster larvae

  1. Cengiz Pehlevan
  2. Paolo Paoletti
  3. L Mahadevan  Is a corresponding author
  1. Harvard University, United States
  2. Simons Foundation, United States
  3. The University of Liverpool, United Kingdom
Research Article
Cite this article as: eLife 2016;5:e11031 doi: 10.7554/eLife.11031
8 figures, 6 videos and 1 table

Figures

Schematic of the model.

(A) Drosophila larvae have segmented bodies. (B) An overview of the model for one segment. Only input neural and proprioceptive signals are shown to the neural controller, its output is not shown. Shades mark subsystems. Red lines show excitatory neural synapses, blue denotes inhibitory synapses. (C) The larva body is modeled as a linear chain of masses, connected by damped linear springs. Head and tail segments are coupled mechanically, denoted by the green line. Each segment feels friction due to contact with the substrate. Body segments are actuated with muscular forces, fi, that are excited by input from the larva VNC. VNC is modeled as a chain of excitatory, Ei, and inhibitory, Ii, neural populations. Self-coupling of populations are not shown. VNC gets proprioceptive input that signals contraction of a particular segment, shown by lines with arrows on both ends. (D) Segment-to-segment propagation of neural activity happens through neural (wEn) and proprioceptive (wEp) couplings. Detailed description and model equations are given in the Model section.

https://doi.org/10.7554/eLife.11031.003
Sustained crawling.

Time is in units of τE. Model is simulated for 500τE, only first 100τE is shown. All simulations were based on Equations (1–5), with parameter values as specified in the Table 1. Shade shows the duration of an example peristaltic wave. (A) Kymograph of body segments. Distance is measured in units of L. (B) Muscular forces in segments. Same color code is used as in the A). (C) Neural activity in segments. Solid line denotes excitatory neuron population activity, and dashed lines denote inhibitory population. Same color code is used as in the A)

https://doi.org/10.7554/eLife.11031.005
Perturbations of VNC.

Top row: E8 is inhibited for t[65,95], shown in purple. Bottom row: I8 is maximally excited in the range t[65,95], shown in purple. Color code and parameters are the same as Figure 1. (A) and (D) Kymograph of body segments. (B) and (E) Muscular forces in segments. (C) and (F) Neural activity in segments. We note that in these simulations, crawling is started at t=0 with an excitatory pulse applied to E6 of the stationary larva, demonstrating that our model allows for the peristaltic wave to start at any segment.

https://doi.org/10.7554/eLife.11031.007
Sustained crawling without proprioception.

The absence of proprioception induces slower crawling. In the lower panels, “p.” denotes crawling with proprioception, 'np.' denotes crawling without proprioception. (A) Kymograph of body segments. (B) Muscular forces in segments. (C) Neural activity in segments. (D) Kymograph of A4 segment (u6) in the full model vs. the model without proprioceptive feedback. (E) Peak contraction of A3-A4 (u5-u6) segmental distance averaged over waves. Here, we plot only one segment interval as in (Hughes and Thomas, 2007) to ease comparison. (F) Phases of (excitatory) neural, muscular and contraction activity in different segments within a wave, with respect to excitatory neuron activity in tail segment. To calculate phases, first Discrete Fourier Transform of the relevant signal is obtained. Phase is the negative complex phase of the fundamental frequency. Contraction of a segment is the difference between its and next anterior neighbor segment’s center of mass displacements.

https://doi.org/10.7554/eLife.11031.010
Proprioception increases robustness of crawling.

Crawling metrics as a function of wEn. In dashed-red, we show the results from the model without proprioceptive feedback (np.), while in blue and black, we show the results with proprioception (p.) based on Equation (1–5) with parameter values as described in the Table 1. (A) Peristaltic waves per unit time (τE). (B) Speed of crawling in units of L/τE. (C) Step size, defined as the tail displacement divided by number of waves. It is measured in units of (L) D) Peak contraction in a segment, averaged over segments and waves. E) Number of simultaneously off-ground segments. This number is calculated at each time step, and the median number across time steps are plotted. (F) Propagation delays through neural and proprioceptive channels (see text for a detailed discussion) are shown. 'n-to-n' denotes neuron propagation delay. 'n-to-p' denotes proprioceptive propagation delay.

https://doi.org/10.7554/eLife.11031.012
Decreasing friction leads to slippage.

(A) Kymograph, muscular forces and neural activity as a function of time for Fmax/kL=0.005. See Figure 2 and text for explanation of plots. (B,C,D,E) Crawling metrics as a function of Fmax/kL. See Figure 5 and text for explanation of plots.

https://doi.org/10.7554/eLife.11031.013
Appendix 1—figure 1
Crawling in a model with only head-tail neural coupling.

(A) Schematic of modified model. (B) Perfectly synchronous driving of E0 and E10. A full kymograph, muscular activity and neural activity. Below the kymograph, the changes in total length of the larva is shown. Color code is the same as Figure 1. (C) Delayed forcing of tail by 0.2π radians. Same figures as B).

https://doi.org/10.7554/eLife.11031.015
Appendix 2—figure 1
Speed vs. friction force for different values of inertia.
https://doi.org/10.7554/eLife.11031.016

Videos

Video 1
GFP imaging of Drosophila larva forward crawling body segment and gut movements.

Courtesy of Ellie Heckscher. See also reference (Heckscher et al., 2012). Original video is available at: https://www.youtube.com/watch?v=1d7zMYWLjLI

https://doi.org/10.7554/eLife.11031.002
Video 2
Crawling simulations of full model larva.

To illustrate the changes in friction, body segments are drawn off the ground when fi exceeds f^ in Equation (5).

https://doi.org/10.7554/eLife.11031.006
Video 3
Crawling simulations of full model larva.

Cycle is started at A4 and temporarily stopped at A6 by inhibiting the excitatory population.

https://doi.org/10.7554/eLife.11031.008
Video 4
Crawling simulations of full model larva.

Cycle is started at A4 and temporarily stopped at A6 by exciting the inhibitory population.

https://doi.org/10.7554/eLife.11031.009
Video 5
Crawling simulations of larva with silenced proprioception.
https://doi.org/10.7554/eLife.11031.011
Video 6
Crawling simulations of larva with low friction.Fmax/kL=0.005.
https://doi.org/10.7554/eLife.11031.014

Tables

Table 1

Dimensionless parameters of our model and their default values used in numerical simulations.

https://doi.org/10.7554/eLife.11031.004
cτE/k3.5fmax/kL5/6τf/τE0.4
Fmax/kL25/3f^/kL5/12τI/τE3
wEE1wEI-2wIE0.6
wII0wEn0.6wEp1.95
wIp1.95E^0.4θ^E,I0.6
u^/L-17/18gn40000gf,p,F1000

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