Skip to main content
SpringerLink
Log in

Biomechanics at the Microscale

  • Chapter
  • First Online:
Combined Discrete and Continual Approaches in Biological Modelling

Part of the book series: Biologically-Inspired Systems ((BISY,volume 16))

  • 308 Accesses

Abstract

Male and female genitalia usually evolve rather quickly and yield remarkable diversity in comparison with other characters. Since natural selection influences shapes indirectly through corresponding properties, links between genital features and their functional mechanisms are critically important, in order to understand evolutionary mechanisms of morphological diversity. In this chapter, we numerically modeled hyper-elongated male and female genitalia especially focusing on their physical properties previously observed in cassidine beetles. These male beetles bear an elongated flagellum and female genitalia have a helically coiled spermathecal duct including some reversal turns called knots. The flagellum was demonstrated to have stiffness gradient, which results in a specific mechanical behavior of the entire copulatory system, because the flagellum stiffness properties might influence its motion within the female spermathecal duct. These properties might be partially due to rubber-like protein resilin that is assumed to be an almost perfect elastomer in insects. Resilin is an ideal material for elastic joints that are subjected to repeated cyclical stress. During the lifetime of an insect, resilin shows neither tearing nor fatigue, when stressed within its natural limits. The resilin, almost unique among biological materials returns back to its original position, when the stress is relieved. In this chapter, the simple sphere-on-the-flat geometry was used in a microindentation experiment as one with the most precise determined boundary conditions. Then the mechanical response of resilin was simulated using a generalized Maxwell model with two characteristic time constants and alternatively using a 1D model with just one characteristic time constant. We also applied newly-developed method of dimension reduction allowing us utilization of functional model along with the generalized Maxwell model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ah-King M, Barron AB, Herberstein ME (2014) Genital evolution: why are females still understudied? PLoS Biol 12:e1001851

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Andersen SO (1963) Characterization of a new type of cross-linkage in resilin, a rubber-like protein. Biochim Biophys Acta 69:249–262

    Article  CAS  PubMed  Google Scholar 

  • Andersen SO, Weis-Fogh T (1964) Resilin. A rubberlike protein in arthropod cuticle. Adv Insect Physiol 2:1–65

    Article  CAS  Google Scholar 

  • Appel E, Gorb SN (2011) Resilin-bearing wing vein joints in the dragonfly Epiophlebia superstes. Bioinspir Biomim 6:046006. (11pp)

    Article  PubMed  Google Scholar 

  • Arnqvist G (1998) Comparative evidence for the evolution of genitalia by sexual selection. Nature 393:784–786

    Article  CAS  Google Scholar 

  • Arnqvist G, Danielsson I (1999) Copulatory behavior, genital morphology and male fertilization success in water striders. Evolution 53:147–156

    Article  PubMed  Google Scholar 

  • Arnqvist G, Rowe L (1995) Sexual conflict and arms races between the sexes: a morphological adaptation for control of mating in a female insect. Proc R Soc Lond B 261:123–127

    Article  Google Scholar 

  • Bailey K, Weis-Fogh T (1961) Amino acid composition of a new rubber-like protein, resilin. Biochim Biophys Acta 48:452–459

    Article  CAS  PubMed  Google Scholar 

  • Bennet-Clark HC, Lucey ECA (1967) The jump of the flea: a study of the energetics and a model of the mechanism. J Exp Biol 47:59–76

    Article  CAS  PubMed  Google Scholar 

  • Bennet-Clark H (2007) The first description of resilin. J Exp Biol 210:3879–3881

    Article  PubMed  Google Scholar 

  • Brennan LR, Prum RO, McCracken KG, Sorenson MD, Wilson RE, Birkhead TR (2007) Co-evolution of male and female genital morphology in waterfowl. PLoS One 5:e418

    Article  Google Scholar 

  • Cheng L, Xia X, Scriven LE, Gerberich WW (2005) Spherical-tip indentation of viscoelastic material. Mech Mat 37:213–223

    Article  Google Scholar 

  • Christensen RM (1982) Theory of viscoelasticity, 2nd edn. Academic, London

    Google Scholar 

  • Cordoba-Aguilar A (2005) Possible coevolution of male and female genital form and function in a calopterygid damselfly. J Evol Biol 18:132–137

    Article  CAS  PubMed  Google Scholar 

  • Dougherty LR, Rahman IA, Burdfield-Steel ER, Greenway EV, Shuker DM (2015) Experimental reduction of intromittent organ length reduces male reproductive success in a bug. Proc R Soc Lond B 282:20150724

    Google Scholar 

  • Eberhard WG (1985) Sexual selection and animal genitalia. Harvard University Press, Cambridge, MA

    Book  Google Scholar 

  • Elliott GF, Huxley AF, Weis-Fogh T (1965) On the structure of resilin. J Mol Biol 13:791–795

    Article  CAS  Google Scholar 

  • Filippov AE, Kovalev AE, Matsumura Y, Gorb SN (2015) Male penile propulsion into spiraled spermathecal ducts of female chrysomelid beetles: a numerical simulation approach. J Theor Biol 384:140–146

    Article  PubMed  Google Scholar 

  • Filippov AE, Kovalev AE, Matsumura Y, Gorb SN (2016) Stiffness gradient of the beetle penis facilitates propulsion in the spiraled female spermathecal duct. Sci Rep 6:27608

    Article  PubMed  PubMed Central  Google Scholar 

  • Filippov AE, Popov VL (2007) Fractal Tomlinson model for mesoscopic friction: from microscopic velocity-dependent damping to macroscopic Coulomb friction. Phys Rev E 75:027103

    Article  CAS  Google Scholar 

  • Geike T, Popov VL (2007) Mapping of three-dimensional contact problems into one dimension. Phys Rev E 76:036710

    Article  CAS  Google Scholar 

  • Gorb SN (2004) The jumping mechanism of cicada Cercopis vulnerata (Auchenorrhyncha, Cercopidae): skeleton-muscle organisation, frictional surfaces, and inverse-kinematic model of leg movements. Arthr Str Dev 33:201–220

    Article  Google Scholar 

  • Gorb SN, Beutel RG (2001) Evolution of locomotory attachment pads of hexapods. Naturwissenschaften 88:530–534

    Article  CAS  PubMed  Google Scholar 

  • Gorb SN, Filippov AE (2014) Fibrillar adhesion with no clusterisation: functional significance of material gradient along adhesive setae of insects. Beilstein J Nanotech 5:837–846

    Article  CAS  Google Scholar 

  • Gorb SN, Beutel RG, Gorb EV, Yuekan J, Kastner V, Niederegger S, Popov VL, Scherge M (2002) Structural design and biomechanics of friction-based releasable attachment devices in insects. Integr Comp Biol 42:1127–1139

    Article  PubMed  Google Scholar 

  • Gosline J, Lillie M, Carrington E, Guerette P, Ortlepp C, Savage K (2002) Elastic proteins: biological roles and mechanical properties. Phil Trans Roy Soc B 357:121–132

    Article  CAS  Google Scholar 

  • Haas F, Gorb SN, Wootton RJ (2000a) Elastic joints in dermapteran hind wings: materials and wing folding. Arthr Str Dev 29:137–146

    Article  CAS  Google Scholar 

  • Haas F, Gorb SN, Blickhan R (2000b) The function of resilin in beetle wings. Proc R Soc Lond B 267:1375–1381

    Article  CAS  Google Scholar 

  • Holwell GI, Winnick C, Tregenza T, Herberstein ME (2009) Genital shape correlates with sperm transfer success in the praying mantis Ciulfina klassi (Insecta: Mantodea). Behav Ecol Sociobiol 64:617–625

    Article  Google Scholar 

  • House CM, Simmons LW (2003) Genital morphology and fertilization success in the dung beetle Onthophagus taurus: an example of sexually selected male genitalia. Proc R Soc Lond B 270:447–455

    Article  Google Scholar 

  • Hosken DJ, Stockley P (2004) Sexual selection and genital evolution. Trends Ecol Evol 19:87–93

    Article  PubMed  Google Scholar 

  • Jensen M, Weis-Fogh T (1962) Biology and physics of locust flight. V. Strength and elasticity of locust cuticle. Philos Trans R Soc B 254:137–169

    Google Scholar 

  • Kamimura Y (2013) Promiscuity and elongated sperm storage organs work cooperatively as a cryptic female choice mechanism in an earwig. Anim Behav 85:377–383

    Article  Google Scholar 

  • Kothari VK, Rajkhowa R, Gupta VB (2001) Stress relaxation and inverse stress relaxation in silk fibers. J Appl Polym Sci 82:1147–1154

    Article  CAS  Google Scholar 

  • van Lieshout E, Elgar MA (2010) Longer exaggerated male genitalia confer defensive sperm-competitive benefits in an earwig. Evol Ecol 25:351–362

    Article  Google Scholar 

  • Kovalev AE. Filippov AE, Gorb SN (2018) Slow viscoelastic response of resilin. J Comp Physiol A 204:409–417

    Article  CAS  Google Scholar 

  • Lombardi EC, Kaplan DL (1993) Preliminary characterization of resilin isolated from the cockroach, Periplaneta americana. Mater Res Soc Symp Proc 292:3–7

    Article  CAS  Google Scholar 

  • Lyons RE, Nairn KM, Huson MG, Kim M, Dumsday G, Elvin CM (2009) Comparisons of recombinant resilin-like proteins: repetitive domains are sufficient to confer resilin-like properties. Biomacromolecules 10:3009–3014

    Article  CAS  PubMed  Google Scholar 

  • Macagno ALM, Pizzo A, Parzer HF, Palestrini C, Rolando A, Moczek AP (2011) Shape – but not size – codivergence between male and female copulatory structures in Onthophagus beetles. PLoS One 6:e28893

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Matsumura Y, Machida R, Mashimo Y, Dallai R, Gottardo M, Kleinteich T, Michels J, Gorb SN, Beutel RG (2014) Two intromittent organs in Zorotypus caudelli (Insecta, Zoraptera): the paradoxical coexistence of an extremely long tube and a large spermatophore. Biol J Linn Soc 112:40–54

    Article  Google Scholar 

  • Matushkina N, Gorb SN (2007) Mechanical properties of the endophytic ovipositor in damselflies (Zygoptera, Odonata) and their oviposition substrates. Zoology 110:167–175

    Article  PubMed  Google Scholar 

  • Michels J, Appel E, Gorb SN (2016) Functional diversity of resilin in Arthropoda. Beilstein J Nanotech 7:1241–1259

    Article  CAS  Google Scholar 

  • Michels J, Gorb SN (2012) Detailed three-dimensional visualization of resilin in the exoskeleton of arthropods using confocal laser scanning microscopy. J Microsc 245:1–16

    Article  CAS  PubMed  Google Scholar 

  • Michels J, Gorb SN, Reinhardt K (2015) Reduction of female copulatory damage by resilin represents evidence for tolerance in sexual conflict. J R Soc Interface 12:20141107

    Article  PubMed  PubMed Central  Google Scholar 

  • Miller GT, Pitnck S (2002) Sperm-female coevolution in Drosophila. Science 298:1230–1233

    Article  CAS  PubMed  Google Scholar 

  • Misak HE, Sabelkin V, Miller L, Asmatulu R, Mall S (2013) Creep and inverse stress relaxation behaviors of carbon nanotube yarns. J Nanosci Nanotech 13:8331–8339

    Article  CAS  Google Scholar 

  • Peisker H, Michels J, Gorb SN (2013) Evidence for a material gradient in the adhesive tarsal setae of the ladybird beetle Coccinella septempunctata. Nat Commun 4:1661

    Article  PubMed  CAS  Google Scholar 

  • Pohrt R, Popov VL, Filippov AE (2012) Normal contact stiffness of elastic solids with fractal rough surfaces for one- and three-dimensional systems. Phys Rev E 86:026710

    Article  CAS  Google Scholar 

  • Popov VL (2010) Kontaktmechanik und Reibung: von der Nanotribologie bis zur Erdbebendynamik. Springer, Berlin

    Book  Google Scholar 

  • Popov VL, Filippov AE (2012) Adhesive properties of contacts between elastic bodies with randomly rough self-affine surfaces: a simulation with the method of reduction of dimensionality. Phys Mesomech 15:324–329

    Article  Google Scholar 

  • Rodriguez V (1994) Function of the spermathecal muscle in Chelymorpha alternans Boheman (Coleoptera: Chrysomelidae: Cassidinae). Physiol Entomol 19:198–202

    Article  Google Scholar 

  • Rodriguez V (1995) Relation of flagellum length to reproductive success in male Chelymorpha alternans Boheman (Coleoptera: Chrysomelidae: Cassidinae). Coleopts Bull 49:201–205

    Google Scholar 

  • Rodriguez V, Windsor DM, Eberhard WG (2004) Tortoise beetle genitalia and demonstrations of a sexually selected advantage for flagellum length in Chelymorpha alternans (Chrysomelidae, Cassidini, Stolaini). In: Jolivet P, Santiago-Blay JA, Schmitt M (eds) New developments in the biology of Chrysomelidae. Academic, The Hague, pp 739–748

    Google Scholar 

  • Rowe L, Arnqvist G (2012) Sexual selection and the evolution of genital shape and complexity in water striders. Evolution 66:40–54

    Article  PubMed  Google Scholar 

  • Sakurai G, Himuro C, Kasuya E (2012) Intra-specific variation in the morphology and the benefit of large genital sclerites of males in the adzuki bean beetle (Callosobruchus chinensis). J Evol Biol 25:1291–1297

    Article  CAS  PubMed  Google Scholar 

  • Santangelo PG, Roland CM (1992) Chain ends and the Mullins effect in rubber. Rubber Chem Technol 65:965–972

    Article  CAS  Google Scholar 

  • Seber GAF, Wild CJ (1989) Nonlinear regression. Wiley, Hoboken

    Book  Google Scholar 

  • Sentenská L, Pekár S, Lipke E, Michalik P, Uhl G (2015) Female control of mate plugging in a female-cannibalistic spider (Micaria sociabilis). BMC Evol Biol 15:18

    Article  PubMed  PubMed Central  Google Scholar 

  • Simmons LW (2014) Sexual selection and genital evolution. Aust Entomol 53:1–17

    Article  Google Scholar 

  • Simmons LW, House CM, Hunt J, Garcia-Gonzalez F (2009) Evolutionary response to sexual selection in male genital morphology. Curr Biol 19:1442–1446

    Article  CAS  PubMed  Google Scholar 

  • Tadler A (1999) Selection of a conspicuous male genitalic trait in the seedbug Lygaeus simulans. Proc R Soc Lond B 266:1773–1777

    Article  Google Scholar 

  • Tanabe T, Sota T (2013) Both male and female novel traits promote the correlated evolution of genitalia between the sexes in an arthropod. Evolution 68:441–452

    Article  PubMed  Google Scholar 

  • Villavaso EJ (1975) Functions of the spermathecal muscle of the boll weevil, Anthonomus grandis. J Insect Physiol 21:1275–1278

    Article  Google Scholar 

  • Weis-Fogh T (1960) A rubber-like protein in insect cuticle. J Exp Biol 37:889–907

    Article  CAS  Google Scholar 

  • Weis-Fogh T (1961) Thermodynamic properties of resilin, a rubber-like protein. J Mol Biol 3:520–531

    Article  CAS  Google Scholar 

  • Weng L, Chen X, Chen W (2007) Rheological characterization of in situ crosslinkable hydrogels formulated from oxidized dextran and N-carboxyethyl chitosan. Biomacromolecules 8:1109–11115

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Willkommen J, Michels J, Gorb SN (2015) Functional morphology of the male caudal appendages of the damselfly Ischnura elegans (Zygoptera: Coenagrionidae). Arthr Struct Dev 44:289–300

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Donetsk Institute for Physics and Engineering, Donetsk, Ukraine

    Alexander E. Filippov

  2. Zoological Institute, Kiel University, Kiel, Germany

    Stanislav N. Gorb

Authors
  1. Alexander E. Filippov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stanislav N. Gorb
    View author publications

    You can also search for this author in PubMed Google Scholar

7.1 Supplementary Electronic Material(s)

(MP4 3095 kb)

(MP4 2380 kb)

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Filippov, A.E., Gorb, S.N. (2020). Biomechanics at the Microscale. In: Combined Discrete and Continual Approaches in Biological Modelling . Biologically-Inspired Systems, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-41528-0_7

Download citation

Publish with us

Policies and ethics

Search

Navigation