Malaria mosquitoes use leg push-off forces to control body pitch during take-off

Abstract

Escaping from a blood host with freshly acquired nutrition for her eggs is one of the most critical actions in the life of a female malaria mosquito. During this take-off, she has to carry a large payload, up to three times her body weight, while avoiding tactile detection by the host. What separates the malaria mosquito from most other insects is that the mosquito pushes off gently with its legs while producing aerodynamic forces with its wings. Apart from generating the required forces, the malaria mosquito has to produce the correct torques to pitch-up during take-off. Furthermore, the fed mosquito has to alter the direction of its aerodynamic force vector to compensate for the higher body pitch angle due to its heavier abdomen. Whether the mosquito generates these torques and redirection of the forces with its wings or legs remains unknown. By combining rigid-body inverse dynamics analyses with computational fluid dynamics simulations, we show that mosquitoes use leg push-off to control pitch torques and that the adaption of the aerodynamic force direction is synchronized with modulations in force magnitude. These results suggest that during the push-off phase of a take-off, mosquitoes use their flight apparatus primarily as a motor system and they use leg push-off forces for control.

Keywords: Anopheles coluzzii; aerodynamics; computational fluid dynamics.

Figure 1

(a) Wake structure visualization using an isosurface with a vorticity threshold of 1,000 s⁻¹, colored by relative pressure. (b) Domain setup: within the circle the solution of a take‐off is shown (see (a)). (c, d) Body and wing geometries used for the simulations, wings are isometrically scaled with length, white dot is the center of mass, green and red dot are the right and left wing roots, respectively. (e, g, h) A mosquito with the right wing in green and left wing in red, viewed from the top (e), side (g) and front (h), including wing kinematics parameters and definition of the stroke‐plane reference frame and world‐reference frame. The wingbeat kinematics parameters are stroke angle γ (e), stroke‐plane angle β, force angle ξ, the wing pitch angle ϕ (g), and the deviation angle θ (h). (f) Free body diagram of a mosquito taking off from a substrate, with the weight vector $\overrightarrow{W}$ in red, and in green the forces produced by the mosquito. These consist of the aerodynamic force produced by the beating wings $\overrightarrow{F}$ _aero, and the ground reaction forces resulting from leg push‐off $\overrightarrow{F}$ _leg [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

The effect of the ground on the aerodynamics of take‐off maneuvers in malaria mosquitoes. (a–d) Maximum air pressure on the ground surface within a take‐off maneuver of a lean mosquito, ((a, b) with and without ground, respectively) and a blood‐fed mosquito ((c, d), with and without ground, respectively). See (k, l) for time at maximum pressure. (e–h) Equivalent wake structures at the point of maximum pressure on the ground, visualized using isosurfaces at the vorticity level of 1,000 s⁻¹, color‐coded with local air pressure; (e) lean mosquito with ground, (f) lean mosquito without ground, (g) fed mosquito with ground, and (h) fed mosquito without ground. (i, j) Integrated pressure over a patch of 2 cm × 2 cm, for the lean and fed mosquito, respectively; light‐gray lines are the aerodynamic forces, green lines are the wingbeat‐average aerodynamic forces, blue lines are the forces exerted by the legs on the ground, and red lines the sum of the leg and wingbeat‐average aerodynamic forces. (k, l) Normalized vertical aerodynamic forces of the lean and fed mosquito, respectively. Orange lines show results for simulations with the ground present, and blue lines are without ground [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3

The kinematics and force dynamics throughout the take‐off of an unfed and blood‐fed malaria mosquito. (a, b) Take‐off dynamics of a lean and blood‐fed mosquito, respectively. The trajectories are shown by the blue curves, red lollipops indicate the body‐axes at intervals of 5 ms, green arrows indicate the aerodynamic force vectors at each time interval, and the dashed gray box indicates the interval when at least one leg is still on the ground. (c, e) Normalized vertical forces for the lean and fed mosquito respectively, where total vertical forces based on the body acceleration are in red, aerodynamic forces throughout the wingbeats are in light‐gray, and the wingbeat‐average aerodynamic forces are in green. (d, f) Angle ξ between the mean aerodynamic force vector and the stroke‐plane for the lean and fed mosquito, respectively; the horizontal dashed line indicates the 90° angle at which the force vector is perpendicular to the stroke‐plane [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4

Kinematics and force dynamics throughout all simulated take‐offs, where all data in blue refer to lean mosquitoes and red data refer to of fed mosquitoes. (a) Take‐off trajectories, with solid line segments show the push‐off phase and dashed line segment show the aerial phase; lollipops show body position and orientation at the end of the trajectory. (b) Average force angle ξ during the push‐off. Asterisk indicates a significant difference (p=.038). (c) Mean normalized vertical force throughout the push‐off phase of simulated take‐offs, separated into total force, aerodynamic force, and leg‐induced push‐off force. (d) The ratio between the mean vertical aerodynamic force and mean vertical total force during the push‐off phase against the normal body weight for all mosquitoes. (e) Average force ratio for the lean and the blood‐fed mosquitoes. (f) Stroke amplitude against the normalized resultant aerodynamic forces. The gray line shows a simple linear regression fit with p<0.0001. (g) Stroke angle amplitude against the deviation angle amplitude. The gray line shows a simple linear regression fit with p<0.0001. (h) Force angle ξ against the normalized resultant aerodynamic force, the gray line is a simple linear regression with p=0.002 [Color figure can be viewed at wileyonlinelibrary.com]

Figure 5

(a, c) Normalized pitch torques throughout the take‐off of a lean and fed mosquito, respectively. Aerodynamic pitch torques throughout each wingbeat are in light‐gray, the equivalent wingbeat‐average aerodynamic torques are in green, and total pitch torques in red. The dashed box indicates the interval when at least one leg is still touching the ground. (b, d, e) Mean pitch torques produced during the push‐off phase of all simulated take‐offs; all data in blue are of lean mosquitoes and data in red are of fed mosquitoes. (b) Normalized average pitch‐up torques and normalized average pitch‐down torques during the push‐off phase. (d) The contribution to the pitch‐up movement throughout the push‐off, of total pitch torque ε_total, aerodynamic pitch torque ε_aero, and leg‐induced pitch torque ε_leg. (e) Pitch angle contribution for the wings (ε_aero) and legs (ε_leg), of lean mosquitoes (blue) and fed mosquitoes (red). All torques and angular momentum were normalized with the product of body weight and body length of the mosquito [Color figure can be viewed at wileyonlinelibrary.com]