Naturwissenschaften

, Volume 100, Issue 12, pp 1163–1169

Consequences of electrical conductivity in an orb spider's capture web

Authors

    • Department of Zoology
  • Donald Edmonds
    • The Clarendon Laboratory
Original Paper

DOI: 10.1007/s00114-013-1120-8

Cite this article as:
Vollrath, F. & Edmonds, D. Naturwissenschaften (2013) 100: 1163. doi:10.1007/s00114-013-1120-8

Abstract

The glue-coated and wet capture spiral of the orb web of the garden cross spider Araneus diadematus is suspended between the dry silk radial and web frame threads. Here, we experimentally demonstrate that the capture spiral is electrically conductive because of necks of liquid connecting the droplets even if the thread is stretched. We examine how this conductivity of the capture spiral may lead to entrapment of charged airborne particles such as pollen, spray droplets and even insects. We further describe and model how the conducting spiral will also locally distort the Earth's ambient electric field. Finally, we examine the hypothesis that such distortion could be used by potential prey to detect the presence of a web but conclude that any effect would probably be too small to allow an insect to take evasive action.

Keywords

SilkElectrostatic chargesAirborne particlesAerosolEarth electric field

Introduction

The typical spider's orb web is suspended by silk frame threads and consists of a capture area where sticky silk threads form a spiral in a wheel of silk ‘spokes’ radiating from a central hub where the spider sits. In cribellate spiders, the capture threads are dry gossamer and consist of hundreds of finest filaments hackled into a wool-like consistency that holds the insect prey using electrostatic charges (Opell et al. 2011a). In the ecribellate spiders, like our garden cross spider, the capture spiral carries a coating of wet silk droplets swollen with water and loaded with a surprisingly strong solution of somewhat unexpected compounds such as GABAmide (γ-aminobutyramide), choline, isethionic acid, N-acetyltaurine and betaine as well as traces of cysteic acid, lysine, serine, glycine, KH2PO4 and KNO3 (Vollrath et al. 1990); finally, there is a good supply of the glycoprotein N-acetylgalactosamine to provide the adhesive glue (Vollrath and Tillinghast 1991). The complex composition makes the coating exceptionally hygroscopic (Vollrath et al. 1990), which functionalizes it to attract water from the atmosphere. While a thread is being spun by the spider, this coating is deposited as a thin and even film (Edmonds and Vollrath 1992). Ambient water rapidly accumulates and leads to an immediate swelling of the coating cylinder, which in turn (via a Plateau–Rayleigh instability) leads to the formation of elongated aqueous droplets distributed evenly along the threads. The droplets have an important double function: they act as functional component providing the windlass mechanism that give this capture thread its very special properties (Vollrath and Edmonds 1989), and they also carry the glue that allows prey to be retained (Opell et al. 2011b; Vollrath and Tillinghast 1991).

A water droplet moving through air charges up electrostatically (Gott 1933), and the ionic charges are highly mobile in the aqueous solution (Richens 1997). A droplet suspended in moving air by a good insulator would charge up equally, and silk is an excellent insulator as has been known (and experimentally used) since Faraday's time. Importantly, airborne particles, including aerosols, pollen and even insects, also become highly charged when moving/flying through the air (Es'kov and Sapozhnikov 1976).

Here, we hypothesize that any charged particle as it approaches the capture thread of a spider's web attracts the charge of opposite sign and repels the charge of the same sign from the glue droplet chain in its vicinity. The charged body and the web would then attract each other electrically.

This phenomenon has practical implications for the web and spider. For example, ecribellate orb webs are exceptionally good at harvesting micron-sized airborne particles (Rachold and Heinrichs 1992) and that could include dangerous pesticide aerosols (Samu et al. 1992). On the other hand, individual web capture threads are clearly attracted to an approaching insect, and the silk will literally ‘spring’ towards it as the insect gets very near (Ortega-Jimenez and Dudley 2013). The mechanism behind this phenomenon relies partly on the charges of both insect and silk droplet and partly on the mechanical properties of the thread, which combines an extremely low modulus with very high extensibility (Vollrath and Edmonds 1989). Because the capture thread is both very soft and extremely stretchy (Köhler and Vollrath 1995, Opell et al. 2008), it requires very little force to distort it, which means that very small electrostatic forces could already have a dramatic effect.

Importantly, the individual droplets on the typical capture thread remain interconnected by narrow necks of liquid (Vollrath and Edmonds 1989; Edmonds and Vollrath 1991). Thus, the aqueous coating, if indeed it was conductive along the length of the capture spiral, could lead to local distortions of the Earth's electrostatic field. We examine this hypothesis theoretically in order to better understand the dynamism of the entire system and its ramifications.

Methods

In order to measure the conductivity of individual spiral threads, we constructed a small Faraday ‘cage’ to fit under a microscope and to hold a 1-cm-long section of capture thread suspended between two metal holders insulated against the cage. These holders could be stretched manually by means of a linear extender. Each metal holder was attached to an ohmmeter capable of measuring the electrical resistance (in gigaohms), and the current flowing was measured as a thread was extended and relaxed while the droplets were simultaneously filmed for later measurements of droplet behaviour and dimensions.

In order to correlate the conductivity of the threads to characteristics of the web, we conducted experiments whereby a metal sphere of 5 mm diameter connected to high DC voltage was slowly approached towards a web or single strands suspended between insulators.

Results and discussion

Previous investigations have shown that the droplets on the capture thread of the common garden cross spider Araneus diadematus seem to be interconnected (Edmonds and Vollrath 1992). Here, we demonstrate that the droplets are indeed interconnected by narrow necks of liquid even when stretched considerably. We simply measured the electrical resistance through a thread as it is stretched while at the same time observing the changing morphology of the droplets. Figure 1 shows that conductivity is a function of stretch, which indicates that the interconnecting necks are thin but never break. Importantly, because of this interconnectivity, the capture thread is conducting along its length. This has significant implications on the function of a whole web, as we shall show later.
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Fig. 1

Resistance measurements of 5-mm sections of A. diadematus web capture spiral as it is being first stretched and then relaxed. The measurements show that the glue droplets are always interconnected by the aqueous coating, which thins but does not break

The theory of ion mobility in an aqueous solution suggests that a capture droplet should always be attracted to an approaching particle, no matter what the charge. To test this assumption for our threads, we conducted a set of experiments where we moved the small metal sphere towards a capture thread and recorded the displacement of web strands caused by its approach. Thus, we measured the effect of a charged particle on (1) a whole web naturally built by the spider in our standard PVC frames (30 × 30 × 5 cm), on (2) a section of web carrying several threads suspended between two insulators and also on (3) 2-cm lengths of single capture spiral threads also suspended between two insulators. The result was always the same: upon approach, the capture web threads were attracted towards the sphere, no matter what the charge (Fig. 2). Thus, the effect was symmetric whether the sphere was connected to a positive or negative voltage, with larger or smaller charges simply having a wider or narrower ‘reach’.
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Fig. 2

Photos showing the distortion of an orb web of A. diadematus by a metallic sphere of radius 5 mm charged to voltages of +1 kV and −1 kV. In a the voltage is positive and in b it is negative demonstrating that the neutral but electricity-conducting web is equally attracted to the charged sphere in both cases. Films of the set-up and phenomenon are shown in the supplementary materials

This demonstrated that in Nature not only individual web capture threads but also whole webs (by the combined action of many threads) would be attracted equally no matter what the sign of the charge on an approaching particle. Thus, in a very real sense, the capture spiral becomes active rather than remains passive and extends to entangle charged prey. Future studies will have to demonstrate (or refute) whether the charges might actively assist the underlying glycoprotein glue dollops circling the core capture spiral deep inside each droplet (Vollrath and Tillinghast 1991) as they stick to insect prey more or less firmly (Opell et al. 2011).

The overall effect of a charged particle approaching a web was calculated by approximating the web by a planar and earthed conducting disk; the force of attraction for a small body of charge q at a perpendicular distance c from the plane becomes FA in the equation below, using the method of images outlined in Bleaney and Bleaney (1989):
$$ {F}_{\mathrm{A}}=\frac{q^2}{4\pi {\varepsilon}_0{\varepsilon}_{\mathrm{R}}{(2c)}^2}, $$
(1)
where ε0 = 8.85 × 10−12 is the permittivity of a vacuum and εR is the relative permittivity of air (Dyer 2004). To a good approximation for air, εR = 1. Note that the force is always attractive no matter what the sign of the charge q because the charged insect always creates a local region on the web with a charge opposite to its own charge. The attractive force FA is directed normal to the plane of the conducting sheet and is long range as it varies as l/c2.
The concept of an enhanced capture of airborne charged particles was calculated from the first principles. On the microscopic scale of airborne particles, which for water particles have radii b ≤ 50 μm, we deal with the attraction between a single conducting glue droplet and the particle. The mechanism of the electrical attraction is the same as described above in that the charged airborne particle induces a charge of opposite sign to its own on a neighbouring glue droplet and is attracted towards it. Thus, the collection efficiency of a given glue droplet for small airborne particles is considerably enhanced. For a typical web of A. diadematus, the supporting silk structure has a diameter of about 1 μm, while the glue droplets on the capture spiral may have diameters of about 20 μm disposed at distances of about 60 μm along the spiral (Edmonds and Vollrath 1992 and unpublished measurements). Both of these dimensional reasons and because of the sticky surface of the glue droplets, the aerosol collection ability of these webs is dominated by the contribution from the glue droplets. In Fig. 3 we depict the induced attractive electrical force between a charged airborne particle of charge q and radius b and an initially uncharged but conducting glue droplet of radius a. We calculate the impact parameter d and the factor of
$$ \mathrm{effective}\ \mathrm{enhancement}={\left(\frac{d}{a+b}\right)}^2 $$
(2)
of the collision cross section of a droplet caused by the electrical attraction. This means that the droplets on the capture spiral have an effective cross section for collecting small airborne charged particles, the effective enhancement factor of (d / a + b)2 larger than the mechanical cross section expected in the absence of the electrical attraction.

The maximum charge on an airborne particle is limited by the breakdown or ionization of the air that surrounds the particle in the electric field created by its charge (Feynman et al. 2013). Ionized air conducts electricity, which will then discharge the particle. Dry air breaks down in an electric field of about Emax = 3 × 106. The application of Gauss's law connects the charge density σ on the surface of a conductor and the electric field E just outside it such that σ = ε0εRE. If the airborne particle is represented by a conducting sphere, the maximum charge density becomes σmax = 2.655 × 10−5 cm−2 so that its total charge becomes q = 4πb2σmax. To obtain estimates for the maximum effect of the electrical interaction, this maximum charge will be assumed for the airborne particles (Jaworek et al. 1998).

Figure 3 shows a conducting sphere of radius a at the origin of the coordinates 0 representing an uncharged but conducting glue droplet on the capture spiral of a web. We represent the airborne particle as a conducting sphere of radius b and carrying a charge q, which approaches parallel to the x-axis with a velocity Vx and at a distance of d from the x-axis. With no electrical effects, the particle will collide with the glue droplet only if d ≤ a + b. However, with an electrical attraction between the particle and the glue droplet, the particle will curve downward as it approaches the origin, as sketched in the figure, and may collide with the droplet even when d is substantially greater than a + b. The limiting case is when the airborne particle just touches the glue droplet tangentially as in the trajectory sketched in the diagram. In this case, the distance d becomes the impact parameter for the collision in that all particles approaching parallel to the x-axis within a cylinder about the x-axis of radius less than or equal to d will strike the droplet. The calculation then becomes a computation of this impact parameter d, knowing the electrostatic attraction between the charged particle and the charge of opposite sign induced in the conduction droplet by the approaching particle.
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Fig. 3

Diagram showing a charged aerosol particle of radius b and a distance R away from a conducting glue droplet of radius a. Far from the droplet, the velocity of the particle is Vx parallel to the x-axis. The electrical attraction between the particle and the glue droplet ensures that the particle curves towards the droplet so that the estimated impact parameter d is considerably greater than a + b, which would be the impact parameter in the absence of the attraction

When the particle is at a position (x,y), a distance R from the origin, the force of electrical attraction F between the charged particle and the charge of opposite sign induced in the conducting droplet may be found using the method of images in Bleaney and Bleaney (1989) and is given in Eq. (3) below:
$$ F=\frac{q^2\left(\frac{a}{R}\right)}{4\pi {\varepsilon}_0{\varepsilon}_R{\left(R-\frac{a^2}{R}\right)}^2}. $$
(3)
When the incoming particle is at a position P with coordinates (x,y) such that the distance from the origin is R, the force acting downward parallel to the negative y-axis in the figure is F sin(θ) and the force acting parallel to the x-axis is F cos(θ) where
$$ \sin \left(\theta \right)=\frac{y}{R}, \cos \left(\theta \right)=\frac{x}{R}\kern0.47em \mathrm{and}\kern0.5em R={\left({x}^2+{y}^2\right)}^{1/2}. $$
(4)
To a good approximation at these speeds, small airborne particles obey Stokes' law such that when acted upon by a force F, they move at a speed V such that Eq. (3) below holds:
$$ F=6\pi b\eta V, $$
(5)
where η = 1.8 × 10−5 is the viscosity of the air at ambient temperatures. The differential equations which determine x and y as a function of the time t are listed below:
$$ \frac{ dx}{ dt}=-{V}_x-\frac{F \cos \left(\theta \right)}{6\pi b\eta}\kern0.5em \mathrm{and}\kern0.5em \frac{ dy}{ dt}=-\frac{F \sin \left(\theta \right)}{6\pi b\eta}, $$
(6)
where F, sin(θ) and cos(θ) are given in Eqs. (1) and (2). These simultaneous first-order differential equations were solved numerically on a computer using Mathcad for various values of a, b, Vx and q, and the limiting value of d was found that just leads to a collision with the glue droplet. The electrostatic attraction has then enhanced the impact parameter from a + b to d. One way of describing this situation would be to say that the effective collision cross-sectional area of each glue droplet on the capture spiral has increased from π(a + b)2 to πd2. The effective cross section for collection of the charged aerosol particles by the glue droplets disposed along the capture spiral has thus been effectively augmented by the effective enhancement factor (d / a + b)2.

To calculate realistic interactions, we assume a fixed glue droplet radius of a = 10 μm based on actual measurements (Edmonds and Vollrath 1992). For an aerosol particle with a radius b = 10 μm and initial drift velocities Vx of 0.01, 0.05 and 0.1 ms−1, the effective enhancement factors were calculated to be 85.3, 31.9 and 23.1, respectively, based on the equations given above. For an aerosol particle of radius b = 20 μm with the same three initial velocities, the effective enhancement factors would become 143.3, 56.1 and 35.4, respectively. This means that the electrical charge on the aerosol particle, interacting with the opposite charge that it induces on the glue droplet, has enhanced the collecting efficiency of each of the glue droplets by these factors.

Importantly, the collecting efficiency of the capture spiral of A. diadematus for airborne aqueous droplets with a distribution of radii up to 50 μm falling under gravity was estimated to be a factor of about 20 greater than that expected from the purely mechanical cross section of the droplets (Samu et al. 1992). Stokes' law predicts (see above) that spherical water droplets of radius 10 and 20 μm in air will fall under gravity with velocities of about 0.012 and 0.048 ms−1. When account is taken of the assumptions made in our theoretical estimates, including that of maximum charge, and the uncertainties due to the distribution of sizes of the aerosol particles in the experiment, the electrical interaction is clearly capable of explaining the enhanced effectiveness of the conducting capture spiral as a collector of small charged airborne particles.

The concept of possible distortion by a conducting web of the Earth's natural electrostatic field was also modeled from the first principles. Our experiments with charged spheres demonstrated that the capture spiral threads extend far outwards towards a charged object depending both on the level of charge and the distance between the two. This suggests that flying insects—typically highly charged from active movement through the air (Warnke 1976)—approaching a web are at danger of being actively captured by threads that actively ‘jump’ forward before active contact (Ortega-Jimenez and Dudley 2013). However, the accumulated charges on the web may have another effect. Importantly, because all droplets are interconnected by narrow necks of liquid, the capture thread is conducting along its length. Thus, it is not only attracted to a charged insect but might also carry a warning if an insect could sense the presence of charges in the environment, as some insects apparently can (Warnke 1976; Greggers et al. 2013; Clarke et al. 2013).

Under stable sunny conditions with clear skies at the surface of the Earth, there exists an electric field of approximately EE = 100 V m−1 pointing downward. During thunderstorms, the electric field may be very much stronger and may even reverse in direction. A spider's orb web with its conducting capture spiral may be considered as a vertical conducting circular disk. Such a conducting disk placed in a previously uniform electric field will distort the electric field. In particular, the static electric field tangential to the surface of any conductor must be zero because the tangential component of an electric field at the boundary between a dielectric material and a conductor is conserved across the boundary, and all static electric fields within the conductor are zero (Bleaney and Bleaney 1989).

We consider the circular web as a thin vertical conducting disk of radius a in the (x,y)-plane of a set of Cartesian coordinates with the origin at the centre of the web and such that the y-axis points vertically downward. The z-axis then forms the axis of the disk through the origin and normal to the plane of the disk while the x-axis is in the plane of the disk and parallel to the surface of the Earth. The electric field of the Earth EE acts vertically downward along the direction of the y-axis. Let us consider an insect flying along the z-axis toward the disk. At a great distance from the disk, the charges induced on the surface of the disk by the downward-pointing electric field do not appreciably change the field EE sensed by the insect. However, as the insect approaches the disk, the downward Earth's field it experiences is reduced by the electric field of the charges induced in the surfaces of the disk until when close to the disk the downward field is reduced to zero. If the insect is capable of sensing the vertical electric field, it could detect the presence of the spider web because it distorts the Earth's field even although it cannot see the web.

The electrostatic problem of such a thin conducting disk, placed in an initially uniform electric field parallel to its plane has been solved (Smythe 1989). The induced charges on each of the two plane faces of the disk may be specified by defining cylindrical coordinates (ρ, ϕ) in the plane of the disk. Here, ρ is the radius vector from the centre of the disk and θ is the angle made between the direction of the radius vector and the direction of the electric field E, which in our case is the angle between ρ and the downward-pointing y-axis. The induced charge per unit area on each face becomes σ (ρ, θ) as below:
$$ \sigma \left(\rho, \phi \right)=\frac{4 Ep{\varepsilon}_0{\varepsilon}_R \cos \left(\phi \right)}{\pi {\left(a{}^2-{p}^2\right)}^{1/2}}. $$
(7)
In a normal downward-pointing Earth's electric field, the lower half of the disk has induced upon it a positive charge and the upper half a negative charge. On the axis of the disk and at a distance z from the disk, the induced charges can be shown to result in an upward-pointing induced electric field EI (E, z) of amplitude given below:
$$ {E}_{\mathrm{I}}\left(E,z\right)=\left(\frac{2E}{\pi}\right)\left[{ \tan}^{-1}\left(\frac{1}{d}\right)-\frac{d}{1+{d}^2}\right], $$
(8)
where d = z/a and a is the radius of the disk.
The total downward-pointing electric field is experienced by an insect, flying towards the web along the z-axis, then becomes Etot = EE− EI (EE, z) so that Etot = EE when d is large and Etot = 0 when d tends to zero, as expected. The total field Etot is shown plotted against d = z/a in Fig. 4. When d = 1, so that z = a, the reduction of the total field is about 18 %, and the field is not reduced to 50 % of the Earth's field until d = 0.44a. The distortion of the Earth's field is seen to be short range and is unlikely to reveal the presence of a web before it is visually seen. This is particularly so as, under trees and bushes where many webs are to be found, the Earth's field is often much reduced and highly irregular because of the electrical conductivity of the vegetation which tends to short out the Earth's electric field (Wan et al. 2012). We deduce that although the electrically conducting spiral of a spider's web will distort the ambient electric field of the Earth, the effect is short range, and it is unlikely to warn insects of its presence especially when located close to the ground near vegetation.
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Fig. 4

A graph of the ratio of the total vertical electric field to the vertical field of the Earth that will be experienced by an insect flying toward a vertical conducting disk of radius a along the axis of the disk. The ratio is plotted against z/a, where z is the distance from the disk. The ratio must be zero very close to the disk, but the effect is local and the ratio is appreciably smaller than 1 only when z/a ≤ 2

Summary and conclusions

We have now demonstrated that the capture spiral threads of certain orb spiders are conductive and remain so even when stretched. In more generic terms, our observations and calculations suggest that particular spider webs can be very efficient collectors indeed of aerosol particles. In practical terms this means that harvesting webs for chemical analysis may prove a useful technique in assessing the extent of ‘pollution‘ by airborne particulates. This strongly supports the data and conclusions of experimental work by Samu and collaborators on pesticide aerosols (Samu et al. 1992) and by others on solid airborne particles (Rachold and Heinrichs 1992). We may conclude that droplet-bearing orb webs can be excellent indicators of air pollution including the presence of heavy metals (Xiao-li et al. 2006). And if such webs are ingested by the spider for recycling (which is common in some spiders), then the animals themselves will become accumulators of such pollutants.

We further demonstrated the natural (biological) relevance to the spider of droplet charging. The highly extensible capture threads carrying a string of mobile charges always in opposition to any approaching object enhance the effectiveness of the threads and thus spring forward when perhaps the insect is so close as to actually see, or otherwise sense, the web. Whether the charges also enhance the capture efficiency of the thread by affecting the glue remains to be demonstrated, but it is not inconceivable that the slapping action of the forward-springing thread may at least provide for a closer initial bond of glue and insect. So far, the measurements by Ortega-Jimenez and Dudley demonstrate that the charges may indeed have significant implications for the capture efficiency of ecribellate (droplet bearing) orb webs by enhancing its active reach (Ortega-Jimenez and Dudley 2013).

Finally, the hypothesis that any web-induced distortions of the Earth's electrostatic field might be sensed by insect prey clearly now needs to be tested empirically. Recent observations and measurements by two independent groups suggest that even very small disturbances of an electrostatic field can be used by flying insects with Greggers et al. (2013) showing that honey bees may use electric field to learn abstract cues, while Clarke et al. (2013) demonstrate that bumblebees use electric fields as floral cues. Clearly, now it remains to be seen whether these insects might also be able to use their e-sensors in order to avoid webs and thus becoming ‘dinner’.

Acknowledgments

We thank the Science and Engineering Research Council of the UK for funding the original study in 1985 and the Air Force Office of Scientific Research (FA9550-12-1-0294) and European Research Council (324607) for funding the recent follow-up analysis by FV. FV also thanks a patient editor, four excellent anonymous reviewers and Sebastien Neukirch for helpful comments. Donald Edmonds sadly passed away last year after a long illness.

Supplementary material

View video
Supplementary Materials Figure 1

Legend: A section of Araneus diadematus capture thread is observed under a microscope seconds after it has been deposited in the web under RH of 55 %. The thread shows the swelling of the coating followed rapidly by the formation of individual droplets evenly spaced. (MP4 43026 kb)

View video
Supplementary Materials Figure 2

Legend : Film showing the distortion of an orb web of Araneus diadematus by a metallic sphere of radius 5 mm charged to a voltage of 5 kV. In (a) the Voltage is positive and in (b) it is negative demonstrating that the neutral but electricity-conducting web is equally attracted to the charged sphere in both cases. (MP4 64550 kb)

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© Springer-Verlag Berlin Heidelberg 2013