Seminar – 4. year

SPIDERS` SUPER-STRONG SILK RELIES ON ITS CRYSTALS

Author: Klara Presečnik

Mentor: prof. dr. Rudolf Podgornik

Ljubljana, January 2010

AbstractSpiders` silk is a natural material with great mechanical properties. Therefore, scientists are trying

to find its secrets. Latest discovery has shown that spiders` silk is a protein, and its good mechanical properties lay in its tertiary structure: beta-sheet nanocrystals. The bonds in the

structure are hydrogen, which are among the weakest bonds, however here in crystals hydrogen bonds brakes one by one and silk fails gracefully. So the scientists have studied this silk failure and with series of computer simulations found out that the strength of spider silk depends on size of

crystals. They found the critical size of around 3 nm. When the crystals are allowed to grow beyond 5nm, the silk becomes weak and loses all the best mechanical properties which made it

interesting.

Contents1 Introduction................................................................................................................................................................ 22 Typical functions of silk ........................................................................................................................................ 33 Silk structure ............................................................................................................................................................. 33.1 Proteins......................................................................................................................................3

3.2 Hydrogen bonds.........................................................................................................................74 Spinning a fibre.......................................................................................................................................................... 74.1 Nucleation..................................................................................................................................8

4.2 Spinning mechanism..................................................................................................................95 Continuum theory of β-sheet nanocrystal................................................................................................... 115.1 Mechanical properties .............................................................................................................11

5.1.1 Comparison with other materials.....................................................................................115.2 Linear elasticity........................................................................................................................126 Beta nanocrystal size effects ............................................................................................................................ 137 Conclusions............................................................................................................................................................... 15References..................................................................................................................................................................... 15

1 Introduction

Everywhere you go, you cannot avoid seeing spider silk. Spiders are found almost everywhere in the world and although you don`t see them, they leave an evidence in form of spider silk. You notice strands, webs or other form of silk. Spiders are the third most abundant type of animals, there are more than forty thousand identified spider species and they all make silk. [1]

But spiders are not interesting because of their abundance, more interesting is their silk. Silk is one of the toughest and most versitile materials known in our world. Because of that exceptional mechanical properties, scientists are trying to implicate it to use for various technological applications and even in medicine. Some major ampullate silk is even toughest than Kevlar [1] and the toughest is the dragline silk from the Golden Orb-Weaving spider (Nephila clavites). Also, spider silk can keep their strength to -40°C. [2]

Silk is a protein that is formed in the cells lining the spiders` silk glands and with processes of transfer inside the spider to the spigots where these molecules hit the air in different forms which depends on their molecular structure. Because of that, there are known many different kind of silk forms. Some spiders` silks are protective, some are used for trapping, some are used for structure of their web, and some are even used for wrapping caught pray or eggs. The most interesting webs are used for capturing high velocity insects, and are therefore constructed with combination of high and low tensile silks. By using different silks and different shapes of webs, spiders are known as very good engineers.

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2 Typical functions of silk Spiders are the only species where spinning silk stayed present over evolution. Even so, different

kinds of silks were evolved to use in different ecosystems or on different occasions. Some spiders therefore evolved more than one silk, yet there are also known those who kept only one.

Typical function of silk for spider are for:✗ Swathing silk : Used for wrapping and immobilisation of prey.✗ Webs: Most recognizable. They are used for catching pray. Silk must by sticky and also very elastic to

catch pray and prevent rebounding off the web. ✗ Draglines: Used to connect the spider to the web and as safety lines. In webs it represents the non-

sticky spokes. ✗ Parachuting or ballooning: It helps spiders to ˝fly˝. Silk is released and caught by the wind and it

lifts the spider in air. Spiders use it to disperse the young or to move to areas with new food sources.

✗ Shelters: Like burrows or nests.✗ Egg-sacs. ✗ Mating : Usually spiders attract a mate by leaving pheromones on web or males transfer their sperm

on webs.

3 Silk structure

3.1 ProteinsProteins are organic molecules, large and complex molecules that play many critical roles in nature.

In spider silk, proteins are their main component. Structure of proteins can be described on four different levels. The first level represents amino acids

that are formed into sequence. Secondary structure is made of primary building blocks such as α-helices and β-sheets. These block are than combined into different structural motifs (protein motifs). Some tertiary protein structures are made of a single domain, some of many domains. Third level is basic classification unit. The last protein structure occurs when several polypeptide chains (subunits) come together into a large macromolecular complex. [3]

Amino acids are small molecules. Every amino acid consists of four groups of atoms clustered around central carbon atom. Three out of four groups are always the same and the fourth varies and distinguishes amino acid from another. The fourth group may consist of a single or many atoms. Because of that, amino acids can vary in size and in the ways to bond to other amino acids. In proteins there are only twenty different amino acids that are commonly found, and only three dominate the chains that make up most silks. These amino acids are glycine, alanine and serine. [1]

Figure 1: Spider silk Amino Acids: a – basic structure, b – glycine, c – alanine, d – serine [1]Amino acids are linked together in chains, but these chains are not static. As amino acids are

linked together, each sequence creates a different three-dimensional proteins structure. And that leads to different protein functional and mechanical properties. When chain is formed it is formed from sequences

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of amino acids, and the sequence has an internal regularity. In silk, the key role in defining the mechanical properties are the two repeats – repeating alanine (poly-Ala) and the glycine-alanine (poly-(Gly-Ala) ) motifs. [2] Examples of sequences of major ampullate silk proteins from two golden orb weaver species are given in Figure 2.

Nephila clavipes MaSp1:GGAGQGGYGGLGXQGAGRGGQGAGA

Nephila inaurata madagascariensis MaSp1GGAGQGGYGGLGSQGAGRGGYGGQGAGA

Figure 2: Amino acids sequences: boxed and underlined motifs contribute to silk`s toughness.[1]

After the chain is linked we get the secondary protein structure. There are two main types of motifs: alpha helix and beta sheet. α-helix is a coiled structure of amino acids. It is a right handed coil or spiral where each amino acid residue corresponds to 100° turn in the helix. Also, all the carbonyl oxygen atoms point in one direction, towards the c-terminal end of the helix. They point towards the nitrogen of the amino acids which is 4 residues away in the sequence. This is how the hydrogen bond is formed. It is formed with two electronegative atoms – the amide N and the carbonyl O. That kind of formation of hydrogen bonds holds the structure assembled. However, this structure is considered slightly weaker that beta sheets, because the hydrogen bond is inside the helix and also can be perturbed to ambient water molecules.

Figure 3: This is the stick representation of α-helix. In red are carbonyl oxygen atoms and in blue are amid nitrogen. In first is seen how red atoms are pointing towards blue and on the second hydrogen bonds between these two amides are represented. As seen on the picture, the hydrogen bond is formed between oxygen and 4 residues departed nitrogen. [3]

Similar structures are the 310-helix and π-helix. They differ from α-helix only in the position of

hydrogen bonds. While in α-helix the bond between amino acids 4 residues away, in 310 helix is three residues and in π-helix 5 residues away.

Beta sheets are another secondary structure that is stabilized with hydrogen bonds. In the β-sheet the amino acids lie in nearly straight line. Short segments of chains are known as β-strands. These strands pack together side by side are forming a sheet of interlocking amino acids, known as β-sheets. Typically repeats span 4-12 amino acids, which defines typical strand length h=1-3nm. [4] An example is on a Figure 4.

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A=alanine,G=glycine,L=leucine,Q=glutamine,R=arginine,S=serine,X=any of small subsety=tyrosine

AAAAA

AAAAA

Figure 4: Stick representation of β-sheet.[3]In this case, hydrogen bonds are not between residues adjacent to each other. Bonds are formed

between two lines, two β- strands. Therefore, a network of hydrogen bonds keeps together different β-strands and forms β-sheet. How strands are connected with hydrogen bonds is implied with the orientation of β-sheets. We have parallel and anti-parallel β-sheets and the best presentation for that is so-called ribbon presentation. In this presentation, β-sheets are represented with arrows, which show the direction of β-sheet that is from N-terminus to C-terminus. When arrows are pointing in same direction, we have a parallel β-sheet, and when they point in opposite directions, the β-sheet is anti-parallel.

Figure 5: On the left are representations of parallel and anti-parallel β-sheets in stick representation and in ribbon representation. In A there is the same sheet like in Figure 4 (parallel), just in context. With yellow are marked sheets and with magenta helices. In B there is anti-parallel sheets in protein structure. In C is representation of beta-hairpin. [3][5]

Because parallelism effects hydrogen bonds, this also effects stability and mechanical properties of a β-sheet. In an anti-parallel arrangement, β-strands alternate direction and inter-strand hydrogen bonds can be planar, which is their preferred orientation. In this orientation connected atoms form two mutual backbone hydrogen bonds to each others flanking peptide groups. This is also known as close pair of hydrogen bonds. And that produces the strongest inter-strands stability.

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B

A

C

In a parallel arrangement stability is lower, because it introduced nonplanarity in the inter-strand hydrogen bonding pattern. Also there is rare to find less than five interacting parallel strands in a motif, which suggest that a smaller number may be unstable. Also, parallel β-sheets are also more difficult to form.

When we just have 2 β-strands anti-parallel to each other, we call this secondary structure a beta-hairpin (also called β-turn). The pair of two β-strands is called a loop. They connect together β-strands, β-strands to α-helices or α-helices to each other, and are therefore a very important secondary structure.

When β-sheets pack together side by side, they form a structure, known as β-sheet crystals. In Figure 6 we see two different sized β-crystals. This represents the tertiary level of protein structure.

Figure 6: β-sheets nanocrystals. [4]

If repeats in strands are ordered, strands can pack very closely together. The way the atoms in β-sheets are locked together helps the protein molecule resist breakage, but because the layers of stacked β-sheets can slide over one another, the protein molecule can also flex. [1]

These β-sheets nanocrystals are then connected in a softer semi-amorphous phase. While anti-parallel β-sheets nanocrstals are very ordered and therefore hold main mechanical properties, semi-amorphous phase is structured with less ordered beta structures, 310-helices and β-turns. Semi-amorphous phase represents the matrix that holds the structure together.

Figure 7: Spider silk protein: β-sheets nanocrystal is connected with semi-amorphous phase.

All these structures together form spider silk fibrils, which are connected into the core of spider silk. Furthermore, fibrils are coated with glycoproteins (for stiffness), salts (as bactericides) and hygroscopic organic compounds that are bactericidal and also plasticize the core of the thread. [7]

Figure 8: Representation of spider silk thread from electron density to β-strands, β-sheet nanocrystal, semi-amorphous phase and silk fibrils. Also there is marked the core and the skin of thread. [4]

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3.2 Hydrogen bonds

Packs of β-strands are bonded together with hydrogen bonds which are one of the weakest chemical bonds known. But because of ordered arrangements and closely packed strands, this weakness is not essential. Even more, when the size of β-sheet nanocrystals is controlled by moderating the reeling speed or by metal infiltration, toughness and strength are modified too. When the size of a crystals are reduced, silk can even exceed steel and other engineered materials in mechanical properties. And when crystals are increased, the weakness of hydrogen bonds is more obvious. [4][5]

When scientists were trying to understand how can weak H-bonds in β-sheets produce such strength and toughness, they made a model of how the number of H-bond in sheets effects mechanical resistance. They realised that clusters of three or four hydrogen bonds that bind together stacks of short β-strands rupture simultaneously rather than sequentially when placed under mechanical stress. If strands had only one or two bonds, the protein could not withstand much force. When using more than four bonds that lead to much-reduces resistance because smaller clusters can withstand more energy. This phenomenom results from thermodynamics of bond. [10]

Other significant properties of hydrogen bonds in proteins are connected with the difference of pulling strength. Pulling hydrogen bonds in different directions is due to differences of strength of hydrogen bonds. Simulations suggest that this anisotropy arises from orientation of β-strands, relative to the force vector. It is suggested that longitudinal shearing of n bonds requires a breaking point equivalent to slightly less than n times the force required to rupture one such bond. When modeling the longitudinal shearing of two anti-parallel beta strands hydrogen bonds were able to stand higher load of forces than when the application of force was loaded orthogonally to the β-strands. The effect causing that was rotation of the hydrogen bonds and leading consequently to their breakup at lower forces in the second model. [11]

4 Spinning a fibreSpiders spin silk with spinnerets, and their there body may contain more that one gland. A typical

spider has seven specialized glands which have different amino acid composition. Amino acids defines proteins and therefore also defines mechanical properties of silk. For different purposes, spiders use silk form different glands. The seven glands are (Figure 9):

✗ The aciniform gland make silk for wrapping the prey. Aciniform silk is two to there times as tough as the other silk.

✗ The cylindriform gland makes the cover silk for the egg sac. This silk is called tubiliform silk. It is the stiffest silk.

✗ The pyriform gland makes silk for attachments and for joining threads.✗ The major ampullate gland provides dragline silk. It is as strong per unit weight as steel, but much

tougher. ✗ The minor ampullate gland provides minor-ampullate silk. It is used for temporary scaffolding

during web construction.✗ The flageliform gland provide the core of the threads of the capture spiral. Capture-spiral silk is

used for capturing lines of the web and are therefore sticky, extremely stretchy and tough.✗ Aggregate gland supplied the threads` coating.

Also, glands are paired together and the number of glands varies among these seven groups. While others are less (2 or 3 pairs), pyroform and aciniform glands are many (in some species there is 200 pyroform and 400 acinoform glands).

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4.1 NucleationIn order for the spider to even make silk it needs the proteins, which the threads are made of. The

process of making threads is therefore conditioned with enough amount of proteins or their part: β-sheets. Therefore, the spinning mechanism of natural silk has two steps. The first is nucleation, the formation of β-sheet units, and the second is rapid extension of β-sheet aggregation. Nucleation is formation of insoluble β-sheets units from soluble random coil. Along this process there are created also a series thermodynamically unfavorable associations of β-sheet units. Once the nucleus forms, further growth of the β-sheet unit becomes thermodynamically favorable. The aggregation growth follows a first order kinetic process with respect to the random coil fibroin concentration. The growth aggregation process is also accelerated with the increase of temperature.

Figure 10: Shematic representation of nucleation and aggregation growth. [12]

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Figure 9: Seven specialized glands and their different amino acid composition of a typical Araneid orb weaver. [7]

4.2 Spinning mechanismThe mechanism for spinning a fiber, therefore to form spider silk, lays in a spider`s spinneret.

Schematic presentation of spider`s dragline spinneret is on Figure 11.

The mayor part represents the so-called “spinning dope”. This is a solution that contains the protein molecules used to make the silk fibre dissolved in water. The sac constitutes the main storage repository that leads, through a “funnel”, to a tapering duct. A duct has tree loops inside a sheat and terminates in the valve. After the valve follows a narrow tubular region that the silk can thread through that exits at the spigot.

The dope production occurs in two zones. The A-zone occupies the tail and the first part of the sac. The A-zone is in Figure 11 marked with A. The solution in A zone contains many small spherical droplets. These droplets flow along the tail and the sac. It secrets the spidroin, the protein forming the coal of the thread. The structure of B zone is in a Figure 11 marked with B. It runs from the widest part of the sac to the funnel. It is composed of a colourless homogeneous viscous liquid that coats the A-zone secretion. Therefore, the B-zone secretes coat proteins. The difference between these proteins is in the structure and the size.

Within the major ampullate gland and the first and the second loop or limp is a liquid crystal phase. Liquid crystallinity allows the viscous silk protein solution to flow slowly through the storage sac and duct, while the molecules form complex alignment patterns. The histology of epithelium of first and second limbs is shown in panel C and D of Figure 11. In this two limbs small forces are changing the form of molecules.

Higher stress is generated during rapid extension, called also “internal drawdown taper”. It is shown on panel X. In the third limb of the duct, the forming thread suddenly stretches, narrows and pulls away from the walls. High stress forces are generated. They bring the dope molecules into alignment and into a more extended conformation. Later the molecules are able to join together with hydrogen bonds. The process is similar to zip fasteners and the conformation becomes anti-parallel. In the start of this process thread can be extra coated, and cells that provide that extra coating are shown in panel L.

Before the thread is pushed in the valve (panel Y), whose function is like a clamp gripping the thread. It is also used like a pump to restart spinning if the internal rapture occurs. After the valve, cells in this part of the duct are specialized for water pumping. For that, cells are tall and designed for that, shown in panel F. After that the thread is gripped by lips of the spigot. These lips are elastic and flexible. They strip the thread off the last aqueous phase to help retain water in the spider, place the thread under tension and push the thread to outside world. [7]

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Figure 11: Schematic presentation of spider`s dragline spinneret. [7]

Before the spider silk is extruded (injected in air), it passes through a long thin duct, where the shearing of the fluid compels protein chains to extend in the direction of the flow. That pushes them closer to each other. This process increased the concentration (supersaturation). When the silk is extruded at the spinneret orifice, the supersaturation increases rapidly with evaporation and this induces the nucleation between protein chains. The driving force of the nucleation of new phases (crystals) is Δμ and is defined as the difference between the chemical potentials mother and crystal of the growth unit in the mother and the crystalline phases. The driving force of nucleation in terms of the supersaturation σ, defined by

=kTln 1 (1)

where k and T represents the Boltzmann constant and temperature, =C i−C i

eq

C ieq and C i and C i

eq

denote the concentrations of solute and the equilibrium concentrations of solute and σ defines the speed of evaporation of silk when extruded at the spinneret. At higher speed silk extrudes faster, so σ is large. Driving force determines the radius of the critical nuclei

r c∝1

= 1kTln 1 (2)

so that the crystallite size is in inverse proportion to ln 1 . Therefore, at higher reeling speed crystallites become smaller.

Because spider silk fibres are not just β-sheets nanocrystals, important properties are also orientation of crystals that form fibres and intercrystallite distance. Both depend on reeling speed. When reeling speed is higher, orientation of crystals along the thread axis is better. For intercrystallite distance we can observe two different directions – equatorial and meridional. Similarly as before the intercrystallite distance is smaller at smaller reeling speed. When the speed is increased, the distance gets larger. When the natural reeling speed for spider (10-20 mms-1) is reached, the orientation of the crystallites reaches an equilibrium value and also the crystallite size reaches its smallest value. Also, at this reeling speed, Young`s modulus and the yield stress attain their maximum values and the breaking stress is improved. [9]

All three were measured and are seen at the Figure 12.

Figure 12: Topographic AFM image of spider dragline silk N. pilipes at different reeling speeds and the proposed model for the corresponding structure change with increasing reeling speed: (a) at 2.5 mms-1, (b) at 25 mms-1, and (c) at 100 mms-1. The direction of thread is indicated by the arrow. (d) At low reeling speed (< 2 mms-1) are less well oriented and the amorphous chains are relaxed. (e) With increasing reeling speed, the crystallites are smaller and better oriented. The intercrystallite distance becomes larger. (f) Further increase of reeling speed (> 10 mms-1) causes nanofibrils to merge further together. Observed “particle size”, indicated by a dashed circle, becomes larger, thus the distance between the crystallites become smaller. [9]

All these geometrical controls that can be easily controlled with only reeling speed depend on structure and composition of spider silk fibers. Furthermore, the natural structure is designed so as to lead to the best mechanical properties. Even so, spiders can control these properties and achieve the desired type of silk.

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5 Continuum theory of β-sheet nanocrystal

5.1 Mechanical properties

Strength is an ability of a material to withstand an applied stress without failure. It depends on materials microstructure. We define two different points in deformation of material. When we reach the point when the material begins to deform and can not be reverse the deformation upon removal of stress, we refer to that point as the yield stress. And when we reach the maximum stress that material can withstand before collapsing, we refer to that point as the ultimate strength. The applied stress may be tensile, compressive or shear.

Stiffness is an extensive material property. It is a resistance of an elastic body to deformation by an applied force along a given set of independent displacements and rotations. Stiffness is defined through the relation of force applied to the body and the produced displacement

k= p (3)

A body may also have rotational stiffness k=M , when we apply moment M on the body and observe

the rotation. It is measured in newton-meters per radian.We can also observe two similar bases and furthermore separate stiffness into the shear and the

torsional stiffness. Shear stiffness is the ratio of applied shear force to shear deformation and torsional stiffness is defined as the ratio of applied torsion moment to angle of twist.

Because stiffness is a property of structure and not of the material, elastic modulus is not the same as stiffness. To find the relation between them, we have to consider not only the material ( E) but also the geometry of observed body.

Resilience of material represents the maximum energy per unit volume of the body that can be stored when deformed elastically. That means that material returns to its original shape after the stress is removed. When stress is removed, the stored energy is recovered.

Toughness is defined as an amount of energy per volume the material can absorb before rupturing. It is a resistance to fracture a of the material when subjected under stress. It is measured in units of J/m³. Mathematically it can be determined by measuring the area underneath the stress-strain curve,

energyvolume

=∫0

f

d , (4)

where ε is strain, εf is the strain upon failure and σ is stress. Toughness is related to strength, but is not the same. Material can be strong and tough or only

strong, because strength indicates how much force the material can support, while toughness indicates how much energy the material can withstand before rupturing.

5.1.1 Comparison with other materials

Spider silk is often compared with other materials such as Kevlar and steel. And although steel is still much stronger that spider silk, spider silk`s advantage is in its weight density. The comparison with Kevlar is made is Table 1.

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Material \ Properties

Diameter [μm]

Tensile breaking strain

Breaking stress [GPa]

Initial modulus [GPa]

Yield stress [GPa]

Breaking energy [kJ/kg]

Spider silk 3.35 ± 0.63 0.39 ± 0.08 1.15 ± 0.06 7.9 ± 1.8 0.15 ± 0.06 165 ± 30

Kevlar 12 0.05 3.6 90 / 33Table 1: Comparison of mechanical properties between spider silk and Kevlar. Spider silk was collected at 20mm/s and 25°C from an adult Nephila edulis female. The comparable data is for Kevlar 81 high tenacity yarn 98 (there is no yield stress because yarn has a single modulus).

From table we can see that Kevlar is 3 times stronger but spider silk is 8 times more extendible and therefore 5 times tougher. [7]

Also, if we would compare the spider silk with steel, we would see that it` s strength of 1.1 Gpa approaches that of typical high tensile engineering steel (1.3 GPa) , but silk have a significantly lower relative density than steel. Relative density for the silk is 1.3 and for the steel 7.8. Thus the silk is by far the stronger material if we compare it on weight basis. [7]

5.2 Linear elasticityThe main mechanical properties of silk represent the ability to resist different kind of forces. For silk

key loading condition of force is lateral loading on β-sheet nanocrystals. The mechanical property characterizing this is the stiffness of silk. To examine these key parameters of silk nanocrystals as a function of size, there are two sets of computational experiments – bending and pull- simulations. In the bending scenario a constants lateral force is applied at one end of the nanocrystals and the other end remains fixed. In the pull-out scenario the ends of nanocrystal are fixed and the force is applied on the centre strand. [4] These kinds of scenarios are described with equations of linear elasticity or better their simplification for a beam: the Bernoulli-Euler equations.

Linear elasticity is a branch of continuum mechanics. In our case it is used for structural analysis to study the behaviour of nanocrystals. For linear elasticity the object is solid and became internally stressed when subjected to loading conditions. Deformations are small and the relationship between stress and strain is linear. It also presumes that the object does not deform plastically, that means that the object does not deform non-reversible.

Elementary equation of isotropic linear elasticity is =Ee . It describes linear relation between strain and product of Young`s modulus and longitudinal strain. Similar for shear stress τ, the response is=G and there is G the elastic shear modulus. [13]

Beam theory is a simplification of linear theory of elasticity. In provides the means to calculate the load-carrying and deflection of a beam. The equation that describes the relationship between the beam`s deflection and the applied load is referred as the Bernoulli-Euler (BE) equation and can be written as

d 2

dy2 EI d 2dy2 =q (5)

In BE equation δ(y) is the deflection of a beam at position y, and q is the distributed load, force per unit length. E is the elastic modulus and I the second moment of inertia around the bending area. Often = y ,q=q y and E and I are constants. [14]

To solve BE equation we need four boundary conditions. For silk crystals we observe deflection of cantilever beam when the beam is supported only at one end. This means that we have a bending scenario. The end at y=0 is fixed, so there is no bending there and the slope is zero, and at the end at y=L the force is loaded. This boundary conditions give the solution

(6) .

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= P6EI 3Ly2− y5

For the bending scenario the constant lateral force is produced at the free end of the beam, so the deformation of the tip is

(7) ,

where P is the total applied force. [4]For pull-out scenario, boundary conditions are changed. Now both ends are fixed and total applied

force is in the centre. Also we have to include the effects of shear deformation, which is important for thick beams. Therefore the extended beam model gives

(8),

where DB=EI , DT=GAS . G is shear moduli and As is the cross-sectional area. The ratio between terms in equation quantifies the relative importance of shear contributions of deformation.

The effective stiffness is defined as (9)

.

With it we compare the size dependence of the stiffness with the results obtained from atomistic simulation, where for small forces keff is independent of the force value. It is calculated from the ratio of force applied to the observed time average of displacement at the tip.

The ratio of the first and second terms in Equation 8 is also defined as shear contribution ratio: (10)

.

It quantifies the relative importance of shear contributions in the deformation for a given beam with constant length and material properties. Thus, when s<1 effect is predominately bending and when s>1 the situation is mainly shear. [4]

6 Beta nanocrystal size effects

To explore the mechanical properties and thus the stiffness of spider silk, we have to take into account that spider silk is made out of β-sheets crystals, therefore, the stiffness of silk depends on the stiffness of nanocrystals. The beam we observed in beam theory is now our nanocrystal, where L represents the size of the crystal. Moreover, the series of nanomechanical experimentes enables us to identify the distribution of strains in nanocrystal.

For β nanocrystal the moment of inertia is I=bh3 /12 and AS=bh . Here b is the base length (related to number of sheets) and h is the height of the cross-section (related to length of a beta-strand). Shear contribution ratio of beta-sheets nanocrystal thus becomes

sL =3DB

L2 DT

=14

Eh2

GL2~h2

L2. (11)

Shear contribution ratio s is a function of size. When nanocrystals get smaller, effect is predominately shear and s is greater than 1. When size of nanocrystals becomes greater, loading scenario becomes predominately bending (s<1). This size effect is the result of material properties and geometry of nanocrystals. That means that shear contribution ratio defines how the stress inside the crystals is contributed and that implicate how the hydrogen bonds inside crystals are loaded. When we have predominately shear scenario (s>1) hydrogen bonds are being sheared, that is, pulled orthogonal to the bonding direction. When s<1, hydrogen bonds are pulled in bonding direction what means stretched in tension. Therefore the critical shear contribution ratio has been defined as the point where shearing and bending scenarios are balanced, that is when s equals 1 (s*=1). By defining that, we can also identify critical

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tip=PL3

3EI

tip=PLDT

PL3

3DB

s=3DB

L2 DT

k eff L= P tip

= LDT

L3

3DB−1

shear transition length scale L≈2.5nm . The shear contribution ratio is independent on the number of sheets (b).

Scientists examined the differences in ultimate strength, elastic energy storage (resilience) and energy dissipation (toughness) capacity of beta sheets crystals because of difference in size of nanocrystals, used the pull-out simulations (Figure 13). ( Experiment was made on Bombyx mori silk in sizes of crystal ranging from L=1.87nm to L=6.56nm). As seen from experimental results (Figure 14) we can conclude that toughness is maximized for systems beyond roughly 3nm (Fig. 14,a) and the ultimate strength and initial stiffness are lower when crystal size raises above 3nm (Fig. 14,b). These results also match the result for critical crystal size ( h≈2.5nm ). This implies that the change in the strain distribution is very important for their fracture behaviour.

Figure 13: Nanocrystals under pull-off simulations of smaller crystal – b (L=2.83nm) and larger crystals – c (L=6.56nm). Seen difference is in bending. Larger crystals fail by bending, which leads to a crack-like flaw formation. In shorter crystals, system respond more rigidly (stiffer) and hydrogen bonds breaks by means of stick-slip motion.[4]

Figure 14: b: Variations of pull-out stress as a function of beta-sheet nanocrystal size L. c: Toughness and resilience as a function of -sheet nanocrystal size L. [4]

We can imply that modulating the strand length could result in more resilient, rigid and tougher structures. However, we also defined that for any given nanocrystal length L there is a minimum strand length h to reach a desired high level of shear contribution ratio s. Also, the effectiveness of each beta strand to carry homogeneous load under shear is limited and is a function of the strand length h. Because hydrogen bonds can work cooperatively in clusters, these clusters are limited to critical number of hydrogen bonds at N ≈4 . This is equivalent to critical strand length h=N L0 , where L0≈3 A is the Cα-distance along a beta strand.

Estimated critical dimensions of beta sheet nanocrystals are then h≈1−2nm andL≈2−4nm and are also matching of typical length of strands formed in spider silk, delivered before.

[4]

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7 ConclusionsSpider silk is an excellent natural material and producing artificial material with similar mechanical

properties requires good knowledge of what spider silk is made of, how these parts are connected and how can we improve these qualities to achieve material that have best properties. And the wish to produce this material lays in many applications that can be used for.

Humans were using this natural material for thousands of years. They used it for stopping bleeding wounds, for fishing lines and nets or more recently in optical targeting devices. So the idea is not new. Similarly great mechanical properties we already have in other materials, like Kevlar. However, the problem in Kevlar is the nature of the production associated with pollution. On the other hand, the production of spider silk is environmentally friendly and silk is biodegradable. When silk can be produced in larger quantities, it could replace Kevlar and other materials in applications like:

• Bullet-proof clothing ,• Wear-resistant lightweight clothing,• Ropes, nets, seat belts, parachutes,• Rust-free panels on motor vehicles or boats,• Biodegradable bottles,• Bandages, surgical thread,• Artificial tendons or ligaments, supports for weak blood vessels. [2]

Production of spider silk is not an easy mission. There was already an attempt to make spider farm and collect silk, but because spiders cannot live together because of their cannibalism, production of silk wasn`t as high as they wanted. Therefore the idea is to produce artificial silk. First we have to produce the protein and there was already success in genetically modifying goats, so that their milk contain the protein necessary to make silk. However, the right process to make the silk fibre with desired properties is still in creation.

References[1] Brunetta, L., C. L. Craig. Spider silk: Evolution and 400 Million Years of Spinning, Waiting, Snagging

and Mating. New Haven and London: Yale university press, 2010.[2] http://www.chm.bris.ac.uk/motm/spider/ (4. 1. 2010)[3] http://www.proteinstructures.com/ (4. 1. 2010)[4] Keten, S., et al., Nanoconfinement controls stiffness, strength and mechanical toughness of

[beta]-sheet crystals in silk. Nature Mater. 9, 359-367 (2010).[5] Vollrath, F., et. al., Strength and structure of spiders` silks. Reviews in Molecular Biotechnology 74,

67-83 (2000).[6] Nova, A., et al., Molecular and nanostructural mechanisms of deformation, strength and toughness

of spider silk fibrils. Nano Lett.10(7), 2626-34 (2010). [7] Volrath, F., David P. Knight, Liquid crystalline spinning of spider silk. Nature 410, 541-548 (2001).[8] Keten, S., et al., Nanostructure and molecular mechanics of spider dragline silk protein assemblies.

J.R. Soc. Interface, 2010., in press, published online June 2, 2010, doi: 10.1098/rsif.2010.0149.[9] Du Ning, et. al., Design of Superior Spider Silk: From Nanostructure to Mechanical Properties.

Biophysical Journal 91, 4528-35 (2006).[10]Science Daily: http://www.sciencedaily.com/releases/2008/02/080214114448.htm (10. 12. 2010)[11]Brockwell, D. J., et al., Pulling geometry defines the mechanical resistance of β-sheet protein.

Nature Structural Biology 10, 731-737 (2003).[12]Guiyang Li, et. al., The natural silk spinning process. A nucleation-dependent aggregation

mechanism? Eur. J. Biochem. 268, 6600-6606 (2001)[13]Asaro, Robert J., Vlado A. Lubarda. Mechanics of Solids and Materials. New York: Cambridge

university press, 2006.[14] Wikipedia: http://en.wikipedia.org (10. 12. 2010)

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