# Essential role of papillae flexibility in nectar capture by bees

^{a}Laboratoire Interfaces & Fluides Complexes, Université de Mons, B-7000 Mons, Belgium;^{b}Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 of CNRS, École Supérieure de Physique et de Chimie Industrielles, 75005 Paris, France;^{c}Laboratoire Matières et Systèmes Complexes (MSC), UMR 7057 of CNRS, Université de Paris, 75006 Paris, France;^{d}Nonlinear Physical Chemistry Unit, Université libre de Bruxelles, 1050 Bruxelles, Belgium;^{e}Laboratoire de Zoologie, Université de Mons, B-7000 Mons, Belgium

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Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved March 28, 2021 (received for review December 11, 2020)

## Significance

Flowers provide the energy resources of bees. In a competitive world, we can hypothesize that flowers attract bees by producing very sweet nectar since it offers the greatest energetic rewards. However, the nectar sugar concentration rarely exceed 60%, and in vivo measurements show that bees capture nectar less efficiently beyond that limit. Here, we explain the physiological origin of this limit based on an elastoviscous mechanism. Most of bees collect the nectar with tongues covered by elongated papillae that open when immersed in a fluid, the opening dynamics determining the amount of nectar collected per lap. At very large sugar concentrations, we found that viscous forces impede the full opening of papillae, reducing the amount of nectar collected.

## Abstract

Many bees possess a tongue resembling a brush composed of a central rod (glossa) covered by elongated papillae, which is dipped periodically into nectar to collect this primary source of energy. In vivo measurements show that the amount of nectar collected per lap remains essentially constant for sugar concentrations lower than 50% but drops significantly for a concentration around 70%. To understand this variation of the ingestion rate with the sugar content of nectar, we investigate the dynamics of fluid capture by *Bombus terrestris* as a model system. During the dipping process, the papillae, which initially adhere to the glossa, unfold when immersed in the nectar. Combining in vivo investigations, macroscopic experiments with flexible rods, and an elastoviscous theoretical model, we show that the capture mechanism is governed by the relaxation dynamics of the bent papillae, driven by their elastic recoil slowed down through viscous dissipation. At low sugar concentrations, the papillae completely open before the tongue retracts out of nectar and thus, fully contribute to the fluid capture. In contrast, at larger concentrations corresponding to the drop of the ingestion rate, the viscous dissipation strongly hinders the papillae opening, reducing considerably the amount of nectar captured. This study shows the crucial role of flexible papillae, whose aspect ratio determines the optimal nectar concentration, to understand quantitatively the capture of nectar by bees and how physics can shed some light on the degree of adaptation of a specific morphological trait.

The ingestion of liquids to stay hydrated is an essential need for living organisms. Various natural strategies have emerged during the course of evolution to transport fluids. Large animals typically use gravity to drink low-viscosity fluids like water (human, birds) or use various methods to counteract gravity such as lapping [feline (1)], ladling [Canidae (2)], or active suction (Bovidae, Equidae). Small animals use instead viscous and capillary suction (butterflies, hummingbirds, etc.), dipping (bees, ants, bats, etc.), or contrasted wetting properties of their body (Namib desert beetle) to capture fluids (3, 4).

Some insects, birds, and small mammals hydrate and feed simultaneously by ingesting nectar. Capturing such a viscous fluid at small scales is a challenge that nectarivores have solved by developing various types of specialized tongues through natural selection leading to the propagation of favorable traits (5). The coevolution of bees and flowers is a well-known example of such mechanisms highlighted by the various shapes of the tongue observed among bee species in relation to the diversity in flower morphology (6). One intuitive example is the correlation between the corolla depth and the tongue length (7⇓⇓–10).

The relation between the nectar sugar concentration and the bees’ tongue morphology is more subtle. Indeed, since the energy content of a given volume of nectar is proportional to its sugar concentration, flowers should a priori produce the sweetest possible nectar to attract bees interested by maximizing their energy intake. However, our in vivo measurements for *Bombus* show that very sweet nectar is not the best for bees. Fig. 1*A* shows images of a *Bombus terrestris* feeding on a sugar solution. The meniscus at the liquid–air interface moves in average at a constant speed, *Bombus* and yields the ingestion rate *B* and *Materials and Methods*). The temporal evolution of the meniscus position *B*, *Inset*). Repeating this experiment at various sugar concentrations, *C*) with a lapping time *D* together with others found in the literature for other bee species (11, 14). Those results show that the ingestion rate of nectar remains essentially constant for sugar concentrations

Two origins can be considered to explain the drop in ingestion rate observed for a concentration near 70%. It could be related either to the difficulty to swallow nectar when its viscosity (*B* allow us to discriminate between both explanations. As the tongue enters the liquid, the meniscus recoils due to the added extra volume composed of the tongue and the remaining noningested fluid (*E* and *F*. Clearly,

The loss of efficiency of the bees’ tongues in capturing very sweet nectar should then be related to its fine structure, which is ignored in previous models (27). The viscous dipping of smooth rods does not account for the drop in ingestion rate. Indeed, since the bees’ lapping period,

The tongue of a bee is composed of a glossa of radius *SI Appendix*). There are approximately 2,500 papillae per square millimeter so that the average distance between them is about *Calliphora erythrocephala*, *Rhodnius*, *Cupiennius salei*, *A* and *B* shows indeed that capillary forces are strong enough to keep the papillae bent in contact with the glossa. This elastocapillary effect is also observed when bees feed on dry sugar since the papillae open well after the protrusion phase and only when enough saliva is secreted to dissolve the sugar (37).

To determine the role of the papillae in the nectar capture, we analyze their in vivo dynamics recorded with an optical microscope fitted with a high-speed camera for *B. terrestris* (*Materials and Methods*). The temporal variations of the position of the tongue tip with respect to the galea, *C*. At low sugar concentration, *C*, the total immersion length of the tongue,

To mimic the opening dynamics of a single papilla, we consider the unbending dynamics of a deflected flexible rod in a viscous fluid. A rod of length L, radius R, Young modulus E, and density *A* and *Materials and Methods*). By varying systematically these control parameters, we show the existence of two regimes: under- and overdamped, separated by a transient stage. Each regime is characterized by distinct scaling for their relaxation times, T, defined as the time at which the rod passes through its rest position for the first time (Fig. 3*B*). For the underdamped regime, where the rod oscillates around its equilibrium position, T is proportional to the oscillation period, whereas in the overdamped regime, there is no oscillation, and T is the time needed for the rod to return to equilibrium.

The theoretical analysis of the rod relaxation dynamics requires to couple the Navier–Stokes and elasticity equations and is unfortunately intractable. Therefore, we propose to decouple the fluid and the rod equations by adding an effective viscous force to the dynamical beam equation (38), which then reads

The expression of the viscous force per unit length, *D*, 2*C*, and 3*B* are obtained with Newtonian fluids [at least up to

Since Eqs. **1** and **2** depend on numerous parameters, it is useful to consider its adimensionalized form. Using **1**:**4** can be solved numerically by imposing that the deflected rod is clamped at *B*).

The relaxation dynamics of the bee’s papillae occur at low values of the ratio *C*):*D*. Notice, however, that to describe the evolution of the ingestion rate as a function of the sugar concentration shown in Fig. 1*D*, a linear approximation for the viscous force could also be used. The difference between the two descriptions is smaller than the typical uncertainty on the in vivo data (*SI Appendix*).

In the overdamped regime, the rod inertia is negligible, and since there is no oscillation, the rod velocity is negative such that **4** with the viscous force [**5**] becomes**6** reduces to two ordinary differential equations:*A*). The nonlinear eigenvalue Eq. **7b** can be solved numerically with **7a**:*D* shows that, when time is properly rescaled, the numerical solutions of Eqs. **4** and **5** at small k and the experimental data in overdamped regime collapse on the asymptotic expression [**8**]. The latter implies that the relaxation time T at which the rod returns to equilibrium (i.e., *B* shows the good agreement between the asymptotic expression [**9**] and experimental data.

By measuring the relaxation time *C*) (16, 19, 20), for *D*, we find **5** is valid. Notice that, since **8**:**9** has been written in a more convenient form with **10** describes the relaxation dynamics of the papillae as shown schematically in Fig. 2*D*. At *D* for *Bombus*, the temporal evolution of *C*).

A model for the nectar capture by bees taking into account the relaxation dynamics of the papillae can now be developed. Since the distance between the papillae is large compared with their radius (

As shown in Fig. 1, bees collect nectar by quickly protracting and retracting their tongue with a constant lapping period, which is the sum of the protraction time, of the retraction time, and of the nectar unloading time. The volume of nectar collected when the tongue retracts out of nectar at **10**). This volume per unit of time, *SI Appendix*). The volume dragged per unit of time by the hairy structure through an LLD mechanism is given by **10**.

At low *D*. The volume captured in this case is thus essentially equal to the volume trapped by the papillae, *A*). Using the measured physiological parameters of *B. terrestris* (Fig. 1*D* and *SI Appendix*), Eq. **11** describes well the in vivo data reported in Fig. 1*D*. A similar quantitative agreement is obtained for *Apis mellifera* when their physiological parameters reported in the literature are used. Fig. 1*D* reveals also a correlation between the ingestion rate, Q, and the total length of the tongue, *D* while keeping all of the other parameters unchanged, Eq. **11** also describes well the data for *Melipona* species.

Fig. 4*A* shows that, for moderate sugar concentrations, the volume of the film dragged through an LLD mechanism is negligible compared with the volume trapped by the papillae, whereas it becomes dominant at large **11** becomes**12** and Fig. 4*A* show a continuous increase of **11**, is therefore a clear signature of the papillae flexibility.

After the ingestion rate is known, the energy intake rate, Ė, can be easily computed using**11**. The dependence of the nectar mass density on the sugar concentration is here taken into account (*SI Appendix*, Eq. **S17**) since Ė varies linearly with *B* shows that Ė is maximum at *Melipona* and *Apis* species and at *Bombus* in agreement with values reported previously (11, 14). Fig. 4*A* shows that the papillae are still open at about 95% of their full erection at those optimal concentrations when the tongue is withdrawn from the nectar [i.e.,

Fig. 4 *A* and *B* shows the existence of two characteristic concentrations: *C*–*E*, the elastoviscous model shows that the concentration

To gain a real insight into the possible variation of *SI Appendix*). Fig. 5*A* shows that L increases linearly with R for all species except the *Eucera* species, which are characterized by more slender papillae. The values of these parameters are then used with Eqs. **10** and **11** to compute *B*). As expected, the value of

The present study explains the role of the papillae in the feeding process for bees. At low sugar concentration, the amount of nectar collected per unit time is essentially constant and controlled by the size of the tongue (i.e., the immersion length

## Materials and Methods

*B. terrestris* from the Biobest firm were used for the in vivo experiments. The colony was kept at the temperature of

### Ingestion Rate.

Before beginning the observation of the drinking process, bumblebees were starved at the room temperature in the dark from 2 to 4 h. A bumblebee was then transferred into a centrifuge tube of 15 mL with a 4-mm hole at the tip. After a habituation phase of 3 min, the extension of the proboscis was motivated by presenting a drop of a solution of diluted honey. Finally, a capillary tube with an inner diameter *Bombus* (48, 49). The experiments were recorded by a camera Logitech C920 at 30 frames per second (Movie S1). The position

### Relaxation Dynamics of Papillae.

Bumblebees were starved from 1 to 2 h before beginning the experiment. A bumblebee was then transferred into a centrifuge tube of 50 mL with a 5-mm hole at the tip where it underwent a habituation phase of 3 min. A sweet solution of known viscosity was placed between two microscope slides spaced by a distance of 1 mm and was presented to the bumblebee. The capture dynamics were recorded under a binocular (Leica MZ16) fitted with a Photron Fastcam Mini AX200 operating at 1,000 frames per second with a 1,024 × 1,024-pixel resolution (Movie S1). The distance *SI Appendix*.

### Relaxation Dynamics of Rods.

Rods made of various materials (steel, polylactide, and polyethylene terephthalate) with length 1.1 cm

The rod was bent by manually displacing its free end by a distance 0.73 mm

### Propagation of Uncertainty.

The uncertainty,

## Data Availability

All study data are included in the article and/or supporting information.

## Acknowledgments

We acknowledge support by Fonds de la Recherche Scientifique Research Grant (Projet de Recherche “ElastoCap”) T.0025.19. We thank J. Bico and B. Abou for helping during the in vivo experiments on the papillae relaxation dynamics, P. Flammang and N. Puozzo for helping during the SEM imaging, and C. Rasmussen for identifying some bee species.

## Footnotes

↵

^{1}Present address: Institut de Physique de Nice, Université Nice Côte d’Azur, CNRS-UMR 7010, 06100 Nice, France.↵

^{2}A.L. and A.D. contributed equally to this work.- ↵
^{3}To whom correspondence may be addressed. Email: fabian.brau{at}ulb.be.

Author contributions: D.M., P.D., and F.B. designed research; A.L., A.D., H.-A.B.H., and F.B. performed research; A.D. and F.B. analyzed data; and P.D. and F.B. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2025513118/-/DCSupplemental.

Published under the PNAS license.

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