# The Strength of Spider’s Silk

The EPSRC, the government funding body that funds mathematical research, requires doctoral candidates to take 100 hours of thought courses at the beginning of their PhD. The University of Manchester has imposed that requirement on all doctoral candidates where the funding source does not explicitly forbid this. Hence I found myself taking the course “Soft Matter Physics” and as part of its evaluation I was required to write an essay on spiders silk, which you will find below.

## The strength of spider’s silk

### 1 Introduction

Spiders are arthropods found on all continents and 45,777 different species have been catalogued [1]. Spider silk outstanding properties have caused prolonged interest in understanding its structure and manufacture. Material properties three times better than kevlar: tensile strengths comparable to steel with elasticity similar to that of rubber while also being biodegradable, hypoallergenic and antimicrobial [2].

Other insects, such as moths, generally use their silk for a single purpose such as cocoons. Spiders employ their silk for a variety of purposes and modify the properties of the silk depending on their intention. Around half of known spiders build webs and more than 130 spider web shapes have been catalogued [23]. Spiders also commonly use silk as lifeline, wrapping of prey and cocoons for the protection of their progeny. However, most research focuses on a small sub-sample of this diversity, in terms of mechanical properties or genetical basis [3]. A oft studied spices is the golden silk spider
Nephila clavipes and the garden cross spider Araneus diadematus [4]. The variety of silks produced by spiders is illustrated in Figure 1, taken from Römer and Scheibel [2].

Figure 1: Illustration of the variaty of silks produced by spiders at the example of the European garden spider Araneus diadematus. The figure is taken from Roemer and Scheibel [2], Figure 1 A).

Orb webs have radial and frame lines made from strong and relatively rigid dragline silk. To satisfy the need to absorb the impact of large(sometimes larger than the spider) prey and ensure that it is ensnared, flag silk is added that provides adhesion and deformability. Flag silk is highly elastic and can withstand impacts of insects such as bees with a diameter of 5 μm or less [2]. While these are but two of the silks produced by spiders, the majority of research has been
focused on examining the chemical make-up and mechanical properties of these two silk types.

Two methods of providing the adhesion of flag line have developed. Cribellate spiders use threats of nanometre diameters in chopped bands to provide elasticity as well as adhesion. Ecribellate spider coat the silk with an aqueous solution, containing organic molecules, fatty acids and glycoproteins, that forms sticky droplets. A more detailed discussion of adhesion is given in Section 3.

In this essay we will review the current state of knowledge of the composition and source of adhesion of spider silks. Spiders silk are a good illustrations of the many effects observed at the nano-scale, combined into a single object and practically used.

### 2 Structure of dragline Silk

Before the turn of the millenia, spider silk was thought to be a protein matrix with embedded crystalline inclusions [56]. More recent investigation has shown a more complex and unusual structure, with long fibriles forming the basis of the macroscopic structure. It is important to remember that spider silks show vast difference in both amino acid content as well as mechanical attributes. Repeated sequences of fibroins, one of the two proteins present in silk, is the basis for the silk of orb-weaving spiders for the past 125 million years [7]. However, the specific amino acid sequences (or motifs) have been shown to differ greatly, to the extend that different species show differences in the relevant genoms [879].

In the spider, concentrated protein solution is stored in the spinning glands, called dope. This is expressed though narrow spinning ducts, where a phase separation takes place. When the silk is physically drawn from these ducts, the threat is rapidly formed. The exact process is still disputed. The repetitive parts of the proteins allow for many, but weak,  interactions in the spinning duct giving rise to macroscopic structure. [10112].

The ends of silk proteins show well defined structure and are made up of hundreds of amino acids and are thought to be crucial in the assembly of the silk due to their ability to form bonds. Repetitive, terminal sequences of different silks and species have been found, showing a shared ancestry [112] .

Amino acids are organic compounds important in biological processes and around 500 have been identified. They are commonly classified according to the location to the core chemical functional group as α, β, γ or δ amino acids. The greek letter numbers the carbon atom starting from the functional group, so β indicates to bond is to the second carbon atom from the functional group. Silk proteins are unusual in that they have amino acid compositions different to common enzymes and that they show very repetitive amino acid sequences in their core. Motifs of tens of amino acids are
repeated up to hundreds of times, forming 90% of the silk protein. These motifs have distinct functional features that contributed to the overall physical properties of the silk [21211]. For some but not all motives, the structure they from in solution as well as in the silk has been found. The macroscopic structure is understood to be composed of four motifs: spacers with unknown function and structure, one motif that is most likely arranged helically, an elastic β-spiral and a crystalline β-sheets. The β-sheet is structural arrangement of proteins where β-stands connect via hydrogen
bonds to form an uneven sheet. A β-spiral is an helical arrangement of β-strands [13].

We can make no intrinsic estimate of the β-sheets elastic modulus but both experimental and molecular dynamics simulation of these nanocrystals exist and indicate that the Young’s Modulus is 16   28 GPa and the shear modulus is 2   4 GPa [41415]. For dragline silk overall, values of the Young’s modulus are reported as 10 GPa [5].

In summary, the silk threat consists of crystalline structures embedded in a rubber like matrix. For dragline silk, the diameter varies between 1 50 μm, depending on species, age, weight and health of the individual.

#### 2.1 Mechanical properties of Silk

The various silks produced by a single spider have vastly different properties. Similar large difference are found between different species. Köhler and Vollrath compared the Araneus diadematus and Uloborus walckenaerius, a ecribellate and cribellate spider respectively [16]. Their study is of specific interest because the authors show great care with the definition of terms and in the experimental implementation. For dragline silk under extension, the stress-strain behaviour can be categorized into four parts. At low extensions (< 5 %), the stress remained small. This was followed by a sharp rise leading to a plateau that lasted to about 15% strain. Beyond this, stress increased linear with strain.

The radial threats break at strain of 0.4, at an engineering stress of 1100 MPa. When stretched to 60 % of their breaking strain, the threats show large hysteresis of 50 % (measured as the difference of the area under the loading and unloading curve) but only 3 % plastic deformation [16].

Let us apply the ideas developed in the lecture course and consider an extension of a matrix of cross-linked strands under uniaxial stress. The relation of tensile stress $\tau$and strain $e$ was found to be

$\tau = n \ k_B \ T \left( (1+e)^2 – \frac{1}{1+e} \right)$

where $n$is the number of strands per unit volume,$k_B$ the Boltzmann constant and $T$ the temperature. This leads to an expression for the Young’s modulus $E$of

$E = 3 \ n \ k_B \ T$

Termonia [17] takes the approach of using synthetic polyethylene as a proxy for spider silk as both of these materials are semicrystalline. For polyethylene the molecular weight between entanglements is found to be of the order of 1500 [18]. The density has been reported as 1.3 kg∕m3 [19]. This gives n 7 1026. Taking room temperature, this leads to an estimate of the Young’s modulus of 9 GPa. This phenomenal agreement with experimentally measured values (10 GPa [5]) is yet more testimony to the power of this approach of understanding the behaviour of such materials.

Termonia goes on to approximate dragline silk as a lattice network with crystalline inclusions. He then deforms this numerically in small increments, finding its minimum energy state after each deformation. He finds good agreement with experimentally reported strees-strain curves in both wet and dry state. This work suggests that the crucial element for understanding the deformation of spider silk is the stiffer β-sheet inclusions.

### 3 The Source of adhesion

Various spiders use adhesion in different ways. For example, moths seldom are entangled in spider webs as their scales easily rub off. The Bolas spider has specialised in catch male moths by mimicking female moth’s attractants and used a drop of glue suspended from a silk threat, called bolas, to catch moths. The bolas spiders manage to entangle moths by
soaking through the scales and adhering to the underlying skin of the moths [2021]. However, little research has been conducted on the physical basis of this specific adhesive process.

Numerous other spiders have evolved surprising uses of adhesion but the most widespread studied are those mentioned in the introduction, that of the Cribellar and Ecribellate spiders. The mechanism of adhesion is a fascinating example of nano-scale physical effects determining larger scale properties.

Cribellar spiders use the cribellum, a broad plate on the spiders abdomium. This is covered with numerous (of the order of 103) spigots, each producing exceedingly thin (nanometer sized) silk [22]. The spider then uses comb like structures on its hind legs to comb out these fibres, hackling them in the process. The combing process causes the fibres to become charged, ensuring that the nanofibres (diameter of around 20 nm) repel each other and form a wool-like yarn. This is then
deposited onto a larger, micron sized threat coming from the same spigots used for other silks. Depending on the species, this is additionally supported by compressed, spring-like fibres from specialised spigots . This process is time consuming for the spiders [23].

The density of the nano-fibres and the surface morphology of the threat are crucial in determining the adhesiveness. Only eleven know species produce cylindrical threats while the other know cribellar spiders (several thousands) form a sequence of regular nodes or puffs [24].

The adhesion has multiple sources. Opell conducted test with five different insects and found the type and density of an insects body hair to influence the stickiness [25]. This indicates that physical entanglement of the nanofibres with insects body hair, similar to that of Velcro, plays a part. However, even on smooth surface, such as a beetle, glass or graphite, the threat adhered, indicating a second mechanism. In that, the behaviour is not unlike that of a gecko’s toe pads.
Proposed explanations included electrostatic attraction, van der Waals forces and hygroscopic forces.

To address the question whether electrostatic forces contribute to the adhesion of the capture silk, Opell [26] conducted a skilful experiment. He attached a single threat to a surface and then measured the force needed to detach it. By choosing substrates of different dielectric constants he established that the electrostatic forces did not play a roles in the adhesion. Hawthorn and Opell [24] went on to verify the effect of hygroscopic forces in a similar manner. For
non-noded threats, the presence or absences of humidity did not affect the attachment to surfaces. However, noded threats (used by the majority of cribellar spiders) did exhibit a dependence on humidity: more force was required to detach them at high levels of humidity.

Hawthorn and Opell concluded that the move from non-noded to noded threats was one of a two-step evolutionary process. The second step being the replacement of the nanofibers with liquid containing glycoprotein glue that is used today by the majority of spiders.

In order to test the hypotheses that that van der Waals forces are responsible for the adherence in non-nodded threats, the experimental results were compared to a simple model of both the van der Waals and capillary forces. The experimental and theoretical results were in good agreement and non-noded threat was found to use van der Waals forces while noded threats were employing both van der Waals as well as hygroscopic forces to adhere to smooth
surfaces. The interaction with the surface happens through the nanofibres. In the noded threat variety, the nodes have a diameter of 35 μm and make contact with the surface at around 170 points/ μm2. The adhesion is generated a numerous, small points of contact who’s force is ineffectually transferred to the axial threat. Experiments of Opell and Hendricks
using plates of contacts of different widths, showed no differences based on width size. This indicates that the adherence stems from the outer edge of the surface only [27].

Most modern spider that produce capture threats are ecribellate spider. They used a water coated threat with glue to work as an adhesive. The proliferation of ecribellate spider compared to their sister linage of the cribellate spiders is often attributed to the superiority of the aqueous glue approach [21]. However, not study investigating this difference and the specific advantages could be found, although the propositions appears reasonable.

Ecribellate spider’s capture threats consists of two axial fibres coated with an aqueous solution of glue. Each axial fibre is produced from its own gland and has two coating glands that secrete the glue around it. The aqueous coat condenses into droplets along the axial threat, similar to pearls on a string, and lose axial threats collect in these droplets. The water soluble fraction of the capture threat does not contain any polymers and the concentration of salt in the coating determines the water uptake. The vapour pressure of this coating is close to ambient humidity found in the natural habitat of the producing spiders. This means the amount of water in the coating is naturally regulated through condensation
from the surrounding. It is notable, given the important roles these salts play in the maintenance of the aqueous coat, that the salts do not crystallize over wide range of vapour pressure. This is distinct from salts we commonly encounter such as sodium chloride [28].

The exact structure of the droplets has been the subject of intense study. Initially a two-phase model was assumed, with glycoprotein acting as glue at the centre of the droplets and a fluid region around it. However, recent observations have lead to the suggestion that the glue occupies three anchored regions. The water plasticizes the silk, hugely contributing to its elastic properties [21].

The droplets also function as windlasses, gathering loose core fibres, keeping the net under tension independent of weather conditions and absorb the large shocks of prey impact [29]. These ”windlasses” are powered by the surface tension of water and prevent the net from sagging even after large plastic deformations [30]. When the string contracts, droplets merge together, and core fibres can be seen to collect into these large droplets. When the threat comes
under tensions, these fibres uncoil and lengthen the threat, causing elastic behaviour driven by surface tension. Extensions of up to 300 % are commonly observed in this silk type [30].

### 4 Conclusion

Spider’s silk has a variety of intriguing physical characteristics: a mechanical strength to weight ratio unmatched by synthetic materials, large deformability and fine tuned mechanisms of adhesions. This short review of current knowledge on the structure and source of adhesion shows that simple model of nano-scale behaviour can be valuable in the comprehension of macro-properties. An understanding of the source of these properties can both point the way of improving man-made materials as well as highlight novel physical effect of soft matter.

Approximately 2’650 Words

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