Landing mosquitoes bounce when engaging a substrate

In this experimental study we film the landings of Aedes aegypti mosquitoes to characterize landing behaviors and kinetics, limitations, and the passive physiological mechanics they employ to land on a vertical surface. A typical landing involves 1–2 bounces, reducing inbound momentum by more than half before the mosquito firmly attaches to a surface. Mosquitoes initially approach landing surfaces at 0.1–0.6 m/s, decelerating to zero velocity in approximately 5 ms at accelerations as high as 5.5 gravities. Unlike Dipteran relatives, mosquitoes do not visibly prepare for landing with leg adjustments or body pitching. Instead mosquitoes rely on damping by deforming two forelimbs and buckling of the proboscis, which also serves to distribute the impact force, lessening the potential of detection by a mammalian host. The rebound response of a landing mosquito is well-characterized by a passive mass-spring-damper model which permits the calculation of force across impact velocity. The landing force of the average mosquito in our study is approximately 40 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μN corresponding to an impact velocity of 0.24 m/s. The substrate contact velocity which produces a force perceptible to humans, 0.42 m/s, is above 85% of experimentally observed landing speeds.

The landing strategies of insects differ from those of vertebrates in both timescale, distance, and speed due to highly contrasting anatomy and function. Insects' immobile eyes and fixed focus optics prevent binocular stereopsis to gauge the distance from a substrate outright 9,36,37 . Insects instead use image motion to determine substrate distance. They monitor object expansion relative to their own motion, and control flight based on the rate of change of perceived object size 11,17 . Honeybees (Apis mellifera) decelerate to a hover 16 mm from a landing surface, demonstrating that touchdown is modulated through relative distance 17,38 , and initiate touchdown with legs on vertical walls whilst pitching their abdomen to dissipate residual flight energy 39 . Similarly, hawkmoths (Macroglossum stellatarum) decelerate upon approaching a flower and hover before initiating touchdown 40 . A female housefly (Musca domestica) approaches a landing surface at a constant velocity until the object reaches a critical size on its retina to induce deceleration 11 . Upon approach to a vertical landing surface, legs extend and bodies pitch upward 7 , most likely as a means to decelerate-flight velocity and pitch are inversely related in houseflies 41 . In contrast, fruit flies (Drosophila melanogaster) accelerate towards their landing surface and, upon touchdown, use leg forces to undergo nearly instant deceleration 8 . Legs extend prior to inverted surface landings and upon touchdown legs also assist in body rotation for multiple appendage engagement 42 .
Detailed Ae. aegypti landing mechanics are absent from literature, to the authors' knowledge, but are likely unique from other insects due to diet, wing mechanics 4 , physiological proportions, and mass. A mosquito has 1-10% the mass of a housefly, honeybee, and hawkmoth 17,43 , and twice that of a fruit flies with dramatically different flight mechanics 44,45 . Mosquito mass allows for survival of collisions with objects of much larger mass traveling at greater speeds 46 , but the influence of mass on landing has not been studied. Typical mosquito flight posture is characterized by fore, mid, and hind-legs raised and splayed, perhaps for the sake of reducing in-flight drag 22 .
In this experimental study we reveal the mechanisms mosquitoes employ to engage hosts with landing forces below which humans can sense 47 . We observe mosquito landings with high-speed cameras, seen in Fig. 1, and digitize their motion to quantify landing forces, the employment of various appendages, and the ability of mosquitoes to cleave to surfaces across a range of contact velocity with a static surface. We begin with a description of our experimental methods in "Experimental methods" section. We initiate "Results" section with a description of the landing sequence and follow with a presentation of kinematics, forces, and energy. We discuss implications of our results in "Discussion" section, and provide concluding remarks in "Conclusion" section.

experimental methods
Mosquito rearing and care. Aedes aegypti eggs were obtained from the United States Department of Agriculture-Agricultural Research Service, Center for Medical, Agricultural and Veterinary Entomology (USDA-ARS-CMAVE, Gainesville, FL) and continued to be cultivated in the Willenberg Lab as described elsewhere 48 . Briefly, 8 mg of eggs ( ∼ 800 eggs) are brushed off the cards and shaken vigorously in a glass vial containing 7.5 mL of larval food in deionized (DI) water (40:60; brewer's yeast and liver powder). The solution is transferred www.nature.com/scientificreports/ into 3 L of DI water in a plastic tray. These trays are incubated at 29-30 • C and larval food is added at day 3 (7.5 mL), day 4 and day 5 (10 mL). At day 6, the larvae/pupae are poured over a 500 µ m strainer, rinsed with fresh DI water and transferred to 200 mL of DI water in 237-mL ( Landing experiments. We film 20 landings of non-blood-fed female Ae. aegypti mosquitoes onto a rigid, vertical surface. Landings are filmed within a plastic 3D-printed flight arena lined with acrylic walls. The arena internally measures ( 70 × 100 × 140 ) mm (H × W × L), as seen in Fig. 1b. A purple substrate, the width of the container and 40 mm in height, is placed at one end of the arena to serve as the landing surface; darker hues elicit landings at a rate 9x higher than clear or white substrates 29 . Mosquitoes are anesthetized with CO 2 for placement into the flight arena, and given sufficient time to recover from anesthetization before filming. To encourage resting mosquitoes into flight, the arena is vibrated at low amplitude 25 Hz for up to 5 s. Vibration does not catapult mosquitoes from walls and mosquitoes are given at least 1 s ( ∼ 600 wingbeats) 2 to recover flight before a landing is considered for analysis. The landing surface protrudes through the walls of the arena and is supported externally such that it does not vibrate with the arena walls. After cessation of vibration, only landings that originate from an orthogonal distance greater than 10 mm is saved for analysis to exclude landings influenced by adjacent wall or neighbor mosquito contact in the moments preceding landing. Landings were recorded on six individual days. Fifty mosquitoes are replaced into the container simultaneously after which multiple landings are recorded-3, 4, 7, 1, 2, 3 landings per recording day, respectively. A new group of 50 mosquitoes is used each filming day. We treat all landings as independent samples and acknowledge the probability of one pseudoreplicate for the entire experimental dataset is 24.6%.
filming. Landings are filmed using Photron AX-100 and UX-100 high-speed cameras at (2000-4000) fps in single and dual camera configurations. All reported kinematic measurements are extracted from single camera experiments for the sake of measurement precision. We view landings from above with a 150-mm Nikon lens and measure the position and velocity in a horizontal plane orthogonal to the landing substrate. Mosquito kinematics are digitized with Open Source Physics Tracker (OSPT) by tracking where the proboscis meets the head in each video frame. OSPT is calibrated with a grid of known dimension in frame and tracks the spatial position of a specified point on the mosquito across frames. Two cameras are utilized for 3D reconstruction to visualize incoming flight path and bouncing sequences as shown in Fig. 1c. In two camera experiments, an additional camera is placed to view the landing surface in its entirety. The cameras are fitted with 60 mm (side) and 24-120 mm (top) Nikon lenses. 3D trajectories are extracted from paired videos with direct linear transformation, DLTdv6 49 . Wing rotation values are taken from videos not used in extracting landing kinematics but instead view mosquitoes top-down.
physical characterization. The proboscis is modeled as an end-loaded cantilever beam. Three proboscises were excised from the head and affixed to a rigid rod with UV-curable glue and filmed within 10-min of excision. A Keyence VHX-900 digital microscope, which has internal pixel calibration, is used to measure proboscis diameter and cantilevered length at a magnification of 150x. The Keyence VHX-900 also films the accumulation of water produced by an ultrasonic humidifier. All deposited moisture except a single droplet is removed manually before measurement. The deflection of the proboscis under the weight of the single droplet is measured optically by photographic measurements in OSPT. The experiment was replicated twice for each proboscis to achieve an average value. Damping characteristics are determined by using a modified cubic flight arena of characteristic length 37.5 mm to inhibit free flight and ground the mosquitoes. The mosquitoes are vibrated at a fixed frequency of 25 Hz and 50 Hz for a few seconds to establish sinusoidal behavior, and then vibration is ceased. Videos are analyzed with OSPT.  Fig. 3a,c (Movie S1). Such a foreleg posture avoids lateral engagement of substrates up to an angle of incidence α = θ legs /2 = 59.2 ± 4.1 • . We limit our scope of analysis to landings in which the angle of incidence of approach is less than α to eliminate landings which were slowed, or otherwise influenced, by grazing contact of aft legs and wings prior to substrate engagement. Mosquitoes approach the test surface with a normal velocity v n = − 0.24 ± 0.14 m/s, N = 20 , as shown in Fig. 2 for t < 0 . Upon tarsal contact with the substrate specimens rapidly decelerate, shown graphically in Figs. 2 and 3a, b. Sensing of the substrate prior to touchdown is likely done with a combination of vision and self-induced pressure wave detection 50 . Encounters with the substrate intermittently occur proboscis first, shown in Fig. 3d  www.nature.com/scientificreports/ two dimensions in Fig. 3a, and pictured in Fig. 3d-g. Only a single trial displayed no bounce. Mosquitoes display a bounce pattern which ceases when tarsal grip is sufficient to overcome bounce acceleration, within 3 bounces (Movie S2). Every bounce and subsequent approach acts to reduce the mosquitoes' incoming momentum by at least 50%, N = 19. With forelimb tarsi securely in place, the abdomen and remaining legs swing downward to contact the surface as the wings cease flapping. Once coming to their resting position, Fig. 3g, wings then rotate inward at an average angular velocity 12, 977 ± 4844 • /s, N = 5 (left wing) and 12, 943 ± 4932 • /s, N = 4 (right wing) to rest atop the abdomen approximately 100 ms after approach, as pictured in Fig. 1a.

Description
While we analyze only landings onto vertical surfaces in this study, we do quantify the frequency of landings onto vertical and horizontal surfaces within our flight chamber. Over the time-course of 5 minutes, beginning at the cessation of arena vibration, we count the number of landings onto the purple substrate when oriented vertical and horizontal, in separate trials. For each trial, 50 female mosquitoes were placed in the arena simultaneously. We count 29 ± 3 , N = 3 , landings on the vertical surface and a meager 3 ± 2 , N = 3 , landings on the horizontally oriented surface, a result which is in line with previous observation of mosquito preference 19 . We note that for many mosquito hosts, humans for example, vertically oriented surface area exceeds that of horizontally-oriented surface area. impact energy and proboscis bending. As legs compress, wings flap, and proboscises deform, mosquitoes absorb their in-flight kinetic energy E k = mv 2 n /2 = 0.061 µ J, where the average mosquito mass m = 1.66 mg, N = 30. In the absence of detailed wing kinematics and computational fluid dynamics, parsing the energy absorbed in the legs U l from that absorbed by the wings U w is not feasible, and is thus beyond the scope of the current study. Therefore, we quantify the energy absorbed U p via proboscis deflection δ p , preceding the initial bounce, seen in Fig. 4a, b (Movie S3). Proboscis deflection is not seen in subsequent bounces and was present in 16 of 20 recorded landings. Altogether we may write E k = U p + U l + U w , and note that potential energy is neglected in our consideration of conservation of momentum in the direction perpendicular to the landing surface.
Deflection of the proboscis δ p is measured approximately 5-80%, N = 16 , of proboscis length L = 1.0 − 2.1 mm. We acknowledge this degree of deformation very likely places the proboscis outside the linear-elastic regime. However, to gain an understanding of the role proboscis deformation plays in the landing process without knowing precise deformed curvature, we employ linear-elastic assumptions. We model the proboscis as an end-loaded cantilever beam where the proboscis deflection stores elastic strain energy U P = k eff δ 2 p /2 and force is applied normal to the beam axis. The effective stiffness of the proboscis k eff can be written in terms of elastic modulus E p , area moment of inertia I = πr 4 /4 = 2.16 × 10 −6 mm 4 , and L, such that k eff = 3E p I/L 3 , where proboscis radius r = 43 ± 2 µ m, N = 3 . The elastic modulus of the proboscis is determined by measuring its deflection δ D under the weight F D of a droplet (see "Experimental methods" section), such that www.nature.com/scientificreports/ where the cantilevered proboscis length ℓ = 917 ± 97 µ m, N = 3 and δ D = 3.2 ± 1.3 µ m, N = 3 . Deflection of a proboscis by a drop can be seen in Fig. 4b, and schematized in Fig. 4c. We measure E p = 1.56 ± 0.16 MPa, N = 3 , and from above, For the maximum observed value of δ p = 0.8L and L = 1 mm, U p = 0.0032 µ J. In the most extreme cases the proboscis is able to absorb up to U p /E k ≈ 5.4% of the kinetic energy of the average mosquito approach. If instead we consider an axially loaded proboscis, the critical buckling load P cr required to produce tip movement δ p , analogous to buckling a column, we calculate P cr = 8.3 µN , well below the human detection threshold, 70 µN 47 . The exact energy calculation associated with buckling would require extensive post-buckling analysis and is complicated by complex material behaviors at large deformation. Such characteristics are not known for proboscises. Recent research in the crushing of slender structures indicates a rapid collapse of load bearing capacity at the onset of instability for even complex structures under both axial and bending loads 51,52 . Conservatively, we assume linear force P degradation such that P = P cr at loading onset and P = 0 at complete collapse. The energy transferred to the proboscis is the sum of the collapse energy U col ≈ P cr L/2 = 0.0042 µ J and the assumed negligible elastic energy. Thus, U col /E k ≈ 6.9% . The agreement in values of U p and U col indicates the primary mechanisms for dissipating energy associated with orthogonal flight motion are leg compression and wing aerodynamics, discussed in "Impact force mitigation by foreleg properties" section. where n is the number of cycles between amplitude measurements x 1 and x 2 equal to unity in our system (Fig. 5a). Solving Eq. (5) Fig. 5b, matching the initial condition x(0) = 2 mm of the data. We note reasonable agreement with experimental data through the first 20 ms of landing. Equation (6) does not capture the influence of aerodynamic damping of the wings, the wing-in-ground effect, and potential coulomb damping in the joints. Moreover, Eq. (6) predicts the mosquito will accelerate slightly, a consequence of modelling legs as damped, outstretched springs.

Impact force mitigation by foreleg properties.
An improved fit may be garnered by prohibiting the virtual spring in the mosquito leg to be extended prior to impact, adding a constant bias C, and phase shift φ, Equation (7) is fit to the raw experimental data in Fig. 5b with a nonlinear least squares solver, where C, D, ζ , ω n , ω d , and φ are free parameters. We plot the best fit provided by Eq. (7) with a red curve in Fig. 5b. The resulting k = 0.07 N/m, c = 1.6 × 10 −4 N-s/m, and ζ = 0.23 agree with those calculated from experiments of mosquito free vibration following an impulsively-stopped vibrating floor [Eq. (5)].
By setting B = x(0) = 0 in Eq. (6) and taking the second time derivative we produce an equation for temporal substrate force that utilizes k, c, and ζ calculated through free vibration experiments, (3) P cr = π 2 E P I 4L 2 , x(t) = C + De (−ζ ω n t) sin(ω d t + φ).
Scientific RepoRtS | (2020) 10:15744 | https://doi.org/10.1038/s41598-020-72462-0 www.nature.com/scientificreports/ A range of ẋ(0) = v n is used to plot F against t in Fig. 6. We plot only the first 10 ms, sufficient time for rebound to begin, as seen in Fig. 5b. We assume the mosquito distributes the load uniformly between two front legs and neglect aerodynamic effects. The slowest mosquito landing provides an impact acceleration of 0.6 gravities, while the fastest impact produces 5.5 gravities. The range of landing velocities in our study is in agreement with in-flight velocities recorded in other studies [53][54][55] . The landing force of the average mosquito in our study is approximately 40 µ N, falling short of human detection. However, covert landings are not universal as 3 trials ( 15% ) record a magnitude of normal velocity greater than that which meets the human force detection threshold 47 , 0.42 m/s. This result aligns with authors' experience of occasionally sensing a landing mosquito, less common than sensing the mosquito bite.

Discussion
Our study reveals Ae. aegypti mosquitoes employ bouncing sequences, leg compression, and proboscis deformation to engage landing surfaces. Unlike bees 38 , houseflies 7 , and fruit flies 8 , we do not witness mosquitoes prepare for landing by adjusting leg posture or body rotation. Their substrate interactions often have head and torso contact with the substrate (Fig. 3e), but the associated forces are easily survivable and relatively small in the insect realm 46 . Proliferation mandates that landings are completed discreetly, below that which a host can sense, so that blood meals are completed unencumbered. Thus a mosquito employs multiple appendages to scrub momentum and reduce the force imparted by any one member. Any flyer, biological or engineered, aiming to land discreetly  where F ′ is the landing force not to be exceeded. For mosquitoes we calculate x eff = 1.4 ± 0.5 mm for initial impact if using F ′ = 70 µ N. This value of x eff would be traveled in ∼ 6 ms, is ≈ 23% of a mosquito body length 22 , and ≈ 33% of the mosquito foreleg, appears exceedingly achievable. Yet, we observe greater compression distances by the proboscis alone, δ P = 1.71 mm, an observation that may be tied to insect perception rather than kinetics. However, it was recently discovered mosquitoes can sense sound pressure waves generated by their flapping wings rebounding from nearby surfaces, a sensory cue that is used to divert from unavoidable surfaces 50 . While the timescale over which landings occur is rapid, it is comparable to the timescale of takeoff 2 and lengthy compared to the timescale of a single wingbeat 56 . Thus, it is possible leg compression at landing is not wholly passive. Active engagement of leg muscles may contribute to the discrepancy between our passive model and experimental response of a landing mosquito. An active force modifier may be added to Eq. (4) to better match mosquito responses, but the magnitude and time-response of such a force is currently unknown and an area for future work. Regardless of active contribution by legs to slow the mosquito, a passive model welldescribes mosquito landing.
The spread posture of mosquito legs during flight (Fig. 1a), the same as upon landing approach, may serve a purpose beyond the previously proposed drag reduction benefits 22 . The oblique angle between the two forward tarsi, θ legs , ensures that approach angles α 60 • toward a vertical surface result in the contact of both forward tarsi. The engagement of the tarsi closest to the substrate induces body rotation to produce foreleg-substrate contact within 8.2 ms. The pliability of a proboscis to absorb impact energy is meager in comparison to the complementary work of legs and wings, and does not obstruct the foreleg tarsi from contacting the surface. The low critical force for proboscis buckling, P cr , allows the mosquito proboscis to collapse in the tangential direction at velocities well below the average value of v n .
We cannot confirm landings onto hosts are representative of those captured in this study, which may be described as controlled crashing. Mosquitoes use a variety of thermal, olfactory, and self-induced airflow cues in addition to vision to track their hosts 50,57 , but it is unclear how non-visual cues aid in clandestine landing. Mosquitoes are also nocturnal, avoiding obstacles invisible to their compound eyes 58 . We have witnessed activity in response to human attractants to be rather uncontrolled crashes when mosquitoes probe nets for passage 19 , suggesting such behavior has no landing intent. Mosquitoes are likewise more qualitatively attracted to purple than the polished and translucent acrylic trialed in preliminary experiments, and previous literature suggests they can easily distinguish solid colors from patterns 23,26,34,35 . The 40-mm high purple landing strip should stand out against its background and change in size as the mosquito approaches. If host landings differ from those on our surface, we expect they produce smaller substrate forces than we calculate as mosquitoes more adequately prepare for impact.

conclusion
In this study we find Ae. aegypti mosquitoes experience bouncing when engaging surfaces to disperse in-flight momentum. In the first bounce, a mosquito will decrease its impact velocity by approximately 50%, and passively rotate its body, by virtue of its in-flight posture, to engage both pairs of fore-and mid-legs. Landings occur in approximately 100 ms from first contact to wing retraction, and are accompanied by proboscis deflection, which crumples as mosquitoes strike surfaces at an average normal-to-substrate speed of 0.24 m/s. The proboscis is able to absorb up to 5.4% of the mosquitoes' initial kinetic energy. Thus, wing aerodynamics and leg compression are the primary mechanisms for kinetic energy dissipation. By treating the mosquito as a simple mass-spring-damper, we find a damping ratio of 0.36 ± 0.10 , indicating mosquitoes behave as an underdamped system when engaging a surface, explaining their propensity for bouncing after their initial, and occasionally, subsequent impacts. Free vibration analysis and the assumption of uniform load distribution among both forelegs indicates landings with normal-to-substrate speeds below 0.42 m/s are undetectable by humans. The landing force of the average mosquito in our study is approximately 40 µ N corresponding to an impact velocity of 0.24 m/s.

Data availability
Raw experimental videos and data are available in perpetuity via Open Science Framework: https ://osf.io/9wkuj /.