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. 2024 Apr 1;35(4):ar47.
doi: 10.1091/mbc.E23-09-0364. Epub 2024 Feb 14.

A modified motor-clutch model reveals that neuronal growth cones respond faster to soft substrates

Laura Pulido Cifuentes  1 , Ahmad I M Athamneh  1 , Yuri Efremov  2   3   4 , Arvind Raman  2   3 , Taeyoon Kim  5 , Daniel M Suter  1   3   6   7   8
Affiliations

A modified motor-clutch model reveals that neuronal growth cones respond faster to soft substrates

Laura Pulido Cifuentes et al. Mol Biol Cell. .

Abstract

Neuronal growth cones sense a variety of cues including chemical and mechanical ones to establish functional connections during nervous system development. Substrate-cytoskeletal coupling is an established model for adhesion-mediated growth cone advance; however, the detailed molecular and biophysical mechanisms underlying the mechanosensing and mechanotransduction process remain unclear. Here, we adapted a motor-clutch model to better understand the changes in clutch and cytoskeletal dynamics, traction forces, and substrate deformation when a growth cone interacts with adhesive substrates of different stiffnesses. Model parameters were optimized using experimental data from Aplysia growth cones probed with force-calibrated glass microneedles. We included a reinforcement mechanism at both motor and clutch level. Furthermore, we added a threshold for retrograde F-actin flow that indicates when the growth cone is strongly coupled to the substrate. Our modeling results are in strong agreement with experimental data with respect to the substrate deformation and the latency time after which substrate-cytoskeletal coupling is strong enough for the growth cone to advance. Our simulations show that it takes the shortest time to achieve strong coupling when substrate stiffness was low at 4 pN/nm. Taken together, these results suggest that Aplysia growth cones respond faster and more efficiently to soft than stiff substrates.

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Figures

FIGURE 1:
FIGURE 1:
Motor-clutch model for adhesion-mediated growth cone advance. (A) Growth cone organization and cytoskeletal components. (B) Motor-clutch model components in cross-section of a single filopodia. (C) Binding of a clutch to F-actin with a constant rate kon. (D) Force-dependent unbinding of a clutch from F-actin with a rate koff. (E) Adhesion reinforcement event that includes the addition of a new clutch at a rate kadd, when at least one of the bound clutches can hold a force of 10 pN.
FIGURE 2:
FIGURE 2:
Experimental approach to study stiffness-dependent adhesion-mediated growth cone advance. (A) Different phases of adhesion-mediated Aplysia growth cone advance using a ConA-coated microneedle with a stiffness of 2 pN/nm (images adapted from Figure 6A of Athamneh et al., 2015). (B) Schematic of the different components of the motor-clutch model in the context of the needle experiment. (C) Kymograph along the line shown in (A). (D) Information about needle tip, C domain boundary, and leading edge displacements as well as F-actin flow rates over time obtained from kymograph shown in (C). The purple vertical line indicates the time when the retrograde actin flow is 20 nm/s, and the pink vertical line shows the time when the C domain starts to advance towards the microneedle.
FIGURE 3:
FIGURE 3:
Parameter optimization. Optimized number of motors and reinforcement constants at different substrate stiffness. The number of motors (nm) and the initial reinforcement rate (kadd0), were optimized for each available experiment at a specific substrate stiffness. The number of experiments used for the optimization was n = 2 for 2.5 pN/nm, 4 pN/nm, and 14 pN/nm, and n = 1 for the rest of substrate stiffnesses. Thus, for the substrate stiffness with n = 2, the filled circles correspond to the average of the average of simulations optimized with each experiment, and the bars corresponds to the SD. x-axis is shown on a log10 scale.
FIGURE 4:
FIGURE 4:
Sensitivity analysis of latency time. Left column: Estimated latency time (tl) plotted versus different specific parameters at the experimental substrate stiffness (left color gradient). On each panel, the optimum value of the corresponding parameter is shown in bold, and for different values of the corresponding parameter the mean and SD from the mean is shown. Right column: Estimated sensitivity of the latency time plotted versus experimental substrate stiffness at different values (right color gradient) for the parameters, which are the same values shown in the x-axis of the corresponding figure in the left column. Moreover, tl and sensitivity are shown only for the parameter values and substrate stiffness when the system is able to reach 20 nm/s, and each point corresponds to the average and standard deviations from simulations. The parameters are displayed from the highest to the lowest sensitivity of the latency time in the following order: A) Clutch spring constant (Kclutch) in pN/nm, (B) force threshold for adding a clutch (Ft) in pN, (C) Myosin stall force (Fs) in pN, (D) Bond rupture force (Fb) in pN. Sensitivity plots on the right are shown with a log10 scale for the x-axis. The rest of the parameters are shown in Supplemental Figure 3.
FIGURE 5:
FIGURE 5:
Sensitivity analysis of substrate deformation. Left column: Estimated substrate deformation at the latency time ∆xsub versus different specific parameters for a specific substrate stiffness (left color gradient). On each panel, the optimum value of the corresponding parameter is shown in bold, and for different values of the corresponding parameter the mean and SD from the mean is shown. Right column: Estimated sensitivity of the substrate deformation at the latency time versus experimental substrate stiffness at different values (right color gradient) for the parameters, which are the same values showed in the x axis of the corresponding figure in the left column. Moreover, ∆xsub and sensitivity are shown only for the parameter values and substrate stiffness when the system is able to reach 20 nm/s, and each point corresponds to the average and standard deviations from simulations. The parameters are displayed from the highest to the lowest sensitivity of ∆xsub in the following order: (A) Single myosin motor stall force (Fs) in pN, (B) unloaded actin flow velocity (vu) in nm/s, (C) multiplication factor for number of myosin motors (nm), (D) multiplication factor for number of myosin motors (nm) and initial number of available clutches (nc0). Sensitivity plots on the right are shown with a log10 scale for the x-axis.
FIGURE 6:
FIGURE 6:
Effect of reinforcement and number of motors on the substrate deformation at 4 pN/nm. Substrate deformation ∆xsub vs time has been plotted for n = 20 simulation trajectories at 4pN/nm with the optimized parameters (Figure 3) and a specific number of motors. (A) Simulations with and without reinforcement with 664 motors. (B) Simulations with and without reinforcement with 1327 motors. (C) Simulations with and without reinforcement with 2654 motors.
FIGURE 7:
FIGURE 7:
Comparison of experimental and simulation results. (A) Comparison of experimental and simulation results for the latency time tl versus substrate stiffness Ksub. (B) Comparison of experimental and simulations results for the substrate deformation ∆xsub at latency time versus substrate stiffness Ksub. The number of experiments used for the optimization was n = 2 for 2.5 pN/nm, 4 pN/nm, and 14 pN/nm, and n = 1 for the rest of substrate stiffnesses. Thus, for the substrate stiffness with n = 2, the filled circles correspond to the average of the average of simulations optimized with each experiment, and the bars corresponds to the SD. x-axis is shown on a log10 scale.
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