Proceedings of the 2nd European Conference on Microfluidics - Microfluidics 2010 - Toulouse, December 8-10, 2010

µFLU10-66

THE ULTRAFAST VALVE OF AN AQUATIC CARNIVOROUS PLANT

Philippe Marmottant∗1, Olivier Vincent1, Catherine Quilliet1, Carmen Weißkopf2, Simon Poppinga2,Tom Masselter2, Thomas Speck2 and Marc Joyeux1

1Laboratoire de Spectromtrie Physique, CNRS / Universite de Grenoble, 140 av. de la Physique, F-38400Saint-Martin d’Heres, France

philippe.marmottant@ujf-grenoble.fr2Plant Biomechanics Group Freiburg, Botanischer Garten der Universitat Freiburg, Schanzlestr. 1, D-79104

Freiburg i.Br, Germany

KEY WORDS

Biomimetics, plant, carnivorous, valve, buckling.

ABSTRACT

A process difficult to perform within the channels of a Lab-on-a-chip is the sudden transfer of a small sample of fluidin a closed container. This operation can be found in the plant kingdom in the aquatic carnivorous Utricularia (whosecommon name is bladderwort). These plants are gifted with tiny suction traps: a slight contact opens their door, thetrap sucks in liquid and the prey hereby. This motion is due to the release of elastic energy stored in the trap body. Wepresent an experimental study, imaging the fast fluid motions under a high-speed camera. We use a laser sheet for intenseillumination in a slice that is few micrometers thick, in order to record fluorescence images at high speed. We found that thedoor buckles inside after triggering, then the suction lasts only half a millisecond, and finally the door closes hermetically.All this open-and-close sequence is performed within a few milliseconds, thus barely visible with the naked eye. The liquidreaches impressive accelerations up to 600 g, preventing any escape of prey animals. We finally discuss how this modelwill prove useful for the design of a biomimetic reproduction of the trap, and its implementation in a microfluidic circuit.

1. INTRODUCTION

1.1 Carnivorous plants

There exist more than 600 species of carnivorous plants, resulting from an adaptation to nutrient-poor habitats[3]. These plants present different kind of traps to catch animals. It is possible to classify these traps into twogroups:

• Passive traps, without a trapping movement, such those from Nepenthes (fig. 1a)• Active traps, such as those from the Dionaea (fig 1b).

A complementary approach between physicists and biologists has recently lead to elucidate the mechanisms ofcertain traps, such as the use of an elastic instability to maximize the speed of capture in Dionaea [1] or thepresence of a visco-elastic fluid in the pitchers of Nepenthes [2].

1.2 Bladderwort (Utricularia spp.)

The bladderworts are a genus of aquatic carnivorous plant that comprises of more than 220 species, includingthe aquatic ones we studied, Utricularia inata, U. vulgaris and U. australis. Numerous biologists have con-tributed to their description and to the elucidation of their mechanism. First studied in the 19th century, theircarnivorous character has been discovered in 1876 [11]. A first detailed study is due to Lloyd [6], who described

∗ Corresponding author

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Proceedings of the 2nd European Conference on Microfluidics - Microfluidics 2010 - Toulouse, December 8-10, 2010

(a) (b)

Figure 1: Two kinds of carnivorous plants (a) Nepenthes with a passive trap (taken from Gaume et al [2]) scalebar is 1cm, (b) Dionaea with an active trap (taken from Forterre et al [1]).

the plant constitution and proposed an electromechanical analogy to describe its behaviour. This model was laterabandoned by the author himself, because of its extreme complexity.

The aquatic plants consist of a long submerse shoot with ramified leaves where the traps are situated. Thetraps, called utricules or bladders, have a size in the order of 1mm (see figure 2).

(a)

trigger

hairs

door or valve

(b)

top

side

front

Figure 2: Description of the trap of the Utricularia (a) Schematic longitudinal section of the trap, taken fromJuniper et al. [3], (b) Spatial orientation of the trap.

It is possible to distinguish two main parts:• the wall consists of only two layers of cells. Its thickness is sensibly constant all over the surface (we

measured 60 micrometers), and increases near the door to form a quasi-circular (ring) rigid structure,whose thicker bottom part is called the threshold.

• the door is attached to the upper part of this ring. The lower free edge of the door is in compression againsta threshold called the velum whose role is to avoid any leaks when the door is closed. The door consistsof only two cell layers, but here thinner than in the wall. The precise structure is complex. Several triggerhairs are located on the door wall, and are responsible for the triggering of the door. The thickness of thedoor is around 15 micrometers.

1.3 Summary of the literature on the trap mechanism

We now sum up a few results that generally admitted concerning the trap mechanism of the bladderwort.

1.3.1 Trap setting

The plant is able to pump water from the inside to the outside of the trap, probably through the action ofglands situated in the wall (internal glands, see [7]). The utricle is waterproof, and this deflates the trap, with a

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Proceedings of the 2nd European Conference on Microfluidics - Microfluidics 2010 - Toulouse, December 8-10, 2010

depression of the water inside as low as 0.17 bars [7]. The time needed to set the trap varies from 30 minutes to4 hours. The plants resist the pressure due to its waterproof door and velum [4].

1.3.2 Trap activation

When a prey triggers the trap by touching one of the trigger hairs situated at the bottom of the door, it opensand water and prey are sucked in. The door then re-closes, which impedes the prey from escaping and rendersthe utricle waterproof again. The capture time is evaluated to be 30 milliseconds approximately [6, 9]. Thedoor opening and closing mechanism remains poorly understood, and two main hypothesis are generally putforward:

• Mechanical hypothesis: the trigger hairs act as levers, and un-block the door, which entails the inflow ofwater, until the pressures are equilibrated again [5].

• Active hypothesis: touching the hair triggers a stimulus that propagates in neighbouring cells, and pro-vokes a softening of the door, that is therefore not able to resist the applied pressure anymore [8]. Mea-surements have shown a change of electrical potential [10], which would corroborate this hypothesis.

The originality and complexity of the trap arise from the fact that, contrary to the other active carnivorousplants that have only a closing phase (such as Dionaea), the trapping action of bladderworts consists of anopening and closing within a fraction of a second.

The comprehension of the trap triggering is limited by several aspects: the observation of ultra-fast phe-nomena, and a modelisation of the physical phenomena at play.

2. Methods

Plants were cultivated indoors, in deionized water, in order to reproduce their natural inhabitat. Traps wereplaced in a Petri dish and were observed under the microscope (up to 10x). The dynamics of the trap werestudied with two kinds of imaging techniques: time-lapse, with a slow camera operated at 1 frame every 100s(0.01 Hz), and high-speed, with a camera that could operate up to 8000 frames per seconds (8000 Hz). Imageanalysis was performed with ImageJ (freeware) and Matlab (Mathworks, Inc.). More details can be found inthe master thesis by Olivier Vincent [12].

3. Results

3.1 Trap setting

We present results obtained from the analysis of image sequences. Seen from the top, it is convenient to evaluatethe volume diminution of the trap measured by its thickness e, at the waist of the trap profile (figure 3). Theshape evolves with time, with an exponential decrease of the thickness (figure 4), with a characteristic time of52 minutes on this measurement.

pumping

triggering

Figure 3: Evolution of the trap profile, monitored by the thickness e,

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Proceedings of the 2nd European Conference on Microfluidics - Microfluidics 2010 - Toulouse, December 8-10, 2010

(a) (b)

FIGURE 3 – (a) Images de la plante dans ses états extrèmes (après déclenchement / après pompage). (b)L’utricule vue comme un cylindre.

gonflé on a donc :!

e(t) = e0 + !e exp(!t/!pompage)!pompage = 52± 2 min

(1)

La précision indiquée est celle de l’ajustement, et !pompage peut varier d’un piège à l’autre. Selon nosobservations, celui-ci reste toujours de l’ordre de 50 min pour nos utricules. Cet ordre de grandeurnous oblige à espacer nos expériences de plusieurs heures pour que les pièges soient toujours dans lemême état lorsqu’on les déclenche.

0 1 2 3 4 5

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

(a)

time (h)

e (

mm

)0 0.5 1 1.5 2 2.5

!3

!2.5

!2

!1.5

!1

!0.5

0

(b)

time (h)

ln (

e!

e0)/!

e

FIGURE 4 – Dégonflement d’une utricule : (a) épaisseur en fonction du temps (b) tracé logarithmique :données (noir), ajustement linéaire pour !pompage = 52 min (rouge).

On peut aussi estimer le débit de pompage maximal (Qp)0 moyennant une hypothèse que nousréutiliserons par la suite : nous considérons la plante comme un cylindre dont la base est une des“joues” de l’utricule, et dont la hauteur correspond à la largeur e mesurée (figure 3(b)). Le volume del’utricule vaut donc V = " (L/2)2 e où L est la longueur du piège (mesurée à environ 1, 5 mm). Cettehypothèse paraît raisonnable compte tenu du fait que l’épaisseur de la plante semble varier de manièrehomogène, au moins lors du début du pompage.

On a donc (Qp)0 = !"

dVdt

#t=0

= !""

L2

#2 "dedt

#t=0

, donc d’après l’équation (1) (Qp)0 = ""

L2

#2 !e!pompage

.Avec les valeurs précédentes, on trouve (Qp)0 " 14 nL/min, du même ordre de grandeur que des débitsdéjà mesurés (21 nL/min dans [13]).

Un apport important de ces mesures est la démonstration du caractère exponentiel du dégonflement.Le mécanisme de pompage de fluide est encore inconnu et nous pourrions dans une approche plus fine

3

Figure 4: Slow deflation of the trap, with an exponential decrease of the trap thickness e towards a plateau valuee0, represented in linear units (a) and in logarithmic units (b).

3.2 Trap suction

The door is triggered manually with the tip of a needle, by touching one of the trigger hairs. We could showthat a very small bending of the trigger hair is enough to trigger the response. The duration of the suction isextremely short: around 2 ms (Fig. 5), fast enough to catch swimming animals.

2 4 6 8 100.3

0.4

0.5

0.6

0.7

(a)

t (ms)

e (

mm

)

2 4 6 8 100

0.05

0.1

0.15

(b)

t (ms)

de

/dt

(m/s

)

FIGURE 9 – Gonflement d’une utricule lors de l’aspiration : (a) épaisseur en fonction du temps (b) sadérivée. L’origine des temps est arbitraire

On peut par exemple estimer la vitesse maximale du fluide : sachant que!

dedt

"max

= 0, 14 m/s, avecles valeurs ci-dessus on obtient umax ! 1 m/s. Nous verrons que ce résultat est en accord avec lesmesures de vitesses présentées en 3.4.

L’utricule engendre donc des mouvements de fluide extrèmement rapides, correspondant aux vi-tesses s’expulsion du sang en sortie du coeur [19].

En mécanique des fluides on caractérise un écoulement par son nombre de Reynolds Re = DU! où

D est une dimension caractéristique de l’écoulement, U une vitesse caractéristique, et ! la viscositécinématique du fluide (! = 10!6 m2/s pour l’eau). Ce nombre compare l’inertie à la diffusion visqueusedans le fluide.

Ici le nombre de Reynolds maximal de l’écoulement est Remax = (2r)umax

! ! 600 12, où ! est la viscositécinématique de l’eau : ! = 10!6 m2/s. L’écoulement est donc fortement inertiel mais reste laminaire (laturbulence apparaissant pour Re " 2000 [2]).

Ceci est compatible avec le tourbillon observé à l’intérieur de l’utricule (voir section 3.1) qui n’estpossible que pour Re# 1 [6].

3.4 Mouvement du fluide

Afin de mesurer directement la vitesse du fluide et de le corréler à l’ouverture de la porte, nousavons visualisé le déclenchement du piège de côté (pour voir la porte) en présence de traceurs dans lefluide.

3.4.1 Choix des traceurs

Nous avons besoin de traceurs de masse volumique semblable à celle de l’eau (densité proche de1) pour éviter une sédimentation trop rapide. De plus il faut trouver un compromis entre une tailleimportante (bien visible au microscope) et une taille petite (qui suit bien l’écoulement du fait d’uneinertie moindre). La résolution de l’ensemble {microscope + caméra rapide} en grossisement 4$ étant del’ordre de 5 µm, nous avons choisi des billes en verre creuses de diamètre compris entre 6 µm et 20 µm.

Si on note u la vitesse du fluide et ub la vitesse d’une bille, la force d’entrainement de Stokes dufluide sur la bille s’écrit Fe = 6"#!rb(ub % u) en régime de faible nombre de Reynolds 13 avec rb rayonde la bille, # et ! respectivement la masse volumique et la viscosité cinématique du fluide. or on peur

12. C’est une contradiction flagrante à l’idée répandue que les écoulements à petite échelle sont à petits nombre de Reynolds !13. En réalité on voit d’après la section 3.3 que la vitesse maximale de l’écoulement est de l’ordre de umax ! 1 m/s, le nombre

de Reynolds associé aux billes croît donc de 0 à environ 10. Le régime de Stokes n’est plus valable pour Rebilles ! 1 mais il nousindique une borne supérieure du temps de relaxation, puisque le frottement est en réalité plus fort qu’un frottement de Stokeset crée donc une relaxation plus rapide.

9

Figure 5: Fast inflation of the plant after trap activation: (a) thickess and (b) speed of inflation.

The aspiration is monitored using tracer particles (hollow glass beads), placed near the door. The maximumfluid velocity measured is extremely high: 1.5 m/s at the largest. The acceleration is also impressive: up to 600g. The fluid motion is therefore dominated transiently by inertia: the Reynolds number computed with thisvelocity and the size of the door (600 micrometers) gives a value of 900. This means we are in the conditionsof a special realm of hydrodynamic flows: high-Reynolds number microfluidics!

We distinguish two zones in front of the door:1. an aspiration zone, where the particles are completely trapped,2. the outer zone, where particles are move due to the suction, but do not enter.

The extent of the zones of aspiration around the door as a radius of around 500 micrometers.

To record the progression of the median door axis during suction we developed a special set-up to image aliving trap. A thin laser illuminates the median door axis as observed in the focused field of view of a microscopeobjective (10x). To obtain the laser sheet, the cylindrical beam from a solid state laser operating at 523nm isexpanded by 10x, its diameter then reaching around 1cm, and then focused in one direction by a cylindrical lensto a few micrometers. Only the orange fluorescence is imaged. Because the laser intensity is high (200 mW)and the trap dyed by infusion in a rhodamin solution for a few minutes, we obtain high-speed fluorescenceimages up to 3000 images per second.The trap is manually activated by touching the trigger hairs with a fine needle. We then see a complete inversionof the curvature of the trap, from convex to concave (Fig. 6a-d), then the door violently opens (Fig. 6e). The

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strong influx of water equilibrates the pressures and the door inverts its curvature (Fig 6f).

We interpret this ultrafast open-and-close mechanism, as a buckling of the spherical shape of the doorunder pressure, then its unbuckling when the pressure difference vanishes.

(a)

door

threshold

(b) (c)

(d) (e) (f)

Figure 6: Recording of the opening and closure of the valve of Utricularia australis. (a) t = 0 ms, initiallyclosed door (b) 5.9 ms, inversion of curvature starts near the threshold (c) 7.6 ms, this inversion spreads (d) 7.9ms, until the whole valve is completely inverted (e) 8.6 ms, the door suddenly opens wide (f) 9.7 ms, and resetsto its initial position.

4. Conclusion and perspectives

A low-speed and high-speed video study revealed the huge dissymmetry of time scales at play during thetrap setting and activation. The trap setting can be interpreted as a storage of elastic energy, and is similar tothe bending of an bow. The release of the energy is violent and occurs within a few milliseconds, suggestinglarge amplitude bifurcation of the behaviour, triggered by touching the hair.. A mechanical lever effect couldexplain the triggering of the metastable trap, but we cannot exclude an electrochemical/physiological process(as in Dionaea) that would account for the extreme sensitivity that we observed. However the door opening andclosing after triggering can be explained by a purely mechanical phenomenon: buckling and unbuckling.

The door opens and closes in a very short time interval of a few milliseconds. In our presentation we willplay high-speed recordings, that help seeing the progression of the door opening and closing. We will show thateven in the absence of manual trigger, small uctuations (from instance by tiny swimming paramecium presentin the medium, or maybe just thermal uctuations noise) were enough to trigger the trap, on average after a delayof 5 hours, with a lot of variations in the delay . The spontaneous activation of the trap was also recorded.

As a perspective, this work is also at the source of a biomimetic inspiration to design a miniature suctionapparatus, helpful to isolate very small quantities of liquid. Indeed, the traps perform an action equivalent tothat of a pipette. The principle of the very fast valve, based on buckling, could be copied with soft elasticmaterials such as the ones used in microuidic devices. The valve is naturally maintained close by the differenceof pressure, and without any external actuation. This biomimetic design of this pipette would thus find its placewithin the realm of Lab-on-chip devices, that need to treat very small amounts of liquid.

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[2] Gaume, L. & Forterre, Y. (2007) A viscoelastic deadly fluid in carnivorous pitcher plants. PLoS ONE,2(11),e1185.

[3] Juniper, B. E. , Robins, R. J., & Joel, D. M. (1989) The carnivorous plants. Academic Press.[4] Lloyd, F. E. (1929) The mechanism of the water tight door of the Utricularia trap. Plant Physiol., 4,87–102.[5] Lloyd, F.E. (1932) Is the door of Utricularia an irritable mechanism. Canadian Journal of Research, 7,386–

425.[6] Francis E. Lloyd. (1942) The carnivorous plants. Chronica Botanica Company, 1942.[7] Sasago, A. & Sibaoka, T. (1985). Water extrusion in the trap bladders of Utricularia vulgaris i. a possible

pathway of water across the bladder wall. Bot. Mat. Tokyo, 98,55–66.[8] Stuhlman, O. Jr & Darder, E. B. (1950) The action potentials obtained from Venus’s Flytrap. Science,

111,491–492.[9] Sydenham, P. H. & Findlay, G. P. (1973) The rapid movement of the bladder of Utricularia sp. Aust. J.

biol. Sci., 26, 1115–1126.[10] Sydenham, P. H. & Findlay, G. P. (1973) Transport of solutes and warter by resetting bladders of utricularia.

Aust. J. Plant Physiol., 2,335–351.[11] Treat, M. (1876) Is the valve of Utricularia sensitive? Harper’s New Monthly Magazine, 52,382–387.[12] Vincent, O.. (2009) Une approche physique du fonctionnement du piege d’une plante carnivore aquatique:

l’utriculaire. Master’s thesis, Universite Joseph-Fourier.

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