Insect jumping, an ancient question

The acrobatic leaps of insects have fascinated both storytellers and scientists for the scope of human history.  Aristophanes wrote in amazement about how far fleas could jump [Ref. 1], suggesting that their jump distance be measured in ‘flea feet’, and compared to the ‘human feet’ of man’s leaps.  Hans Christian Anderson likewise marvelled at jumping insects, writing a cautionary tale of a contest between a flea, a grasshopper, and a tuna. In his tale, both the flea and the grasshopper lose the contest, not because they jumped insufficiently high, but because the judge unfairly preferred the tuna’s manners over the much greater jumping distances of the two insect contestants [Ref. 2]. In any fair contest, however, it would be hard to argue that insects are not the most incredible jumpers of the natural world – with fleas able to launch themselves through the air at speeds of over 2 meters per second [Refs. 3, 4], grasshoppers reaching speeds as fast as 4 meters per second [Ref. 5], and the champion jumpers, planthoppers, reaching speeds as fast as 6 meters per second [Ref. 6]. The times to reach these speeds are breath-takingly short, with grasshoppers able to reach this speed in less than 20 milliseconds, and fleas and planthoppers able to achieve this feat in less than one millisecond. This is far from easy, as these jumps require the insect to navigate three extremely difficult biomechanical challenges: 1) generating the necessary power, 2) directing the power through the legs to generate a controlled jump, and 3) synchronizing the two legs so that differential leg extension does not cause the animal to spin out of control. To solve these problems, evolution has developed biological structures that are strikingly similar to the man-made devices: composite bows, mechanical linkages, and most surprisingly, gears.     

Gregory Sutton received his education at Case Western Reserve University in Cleveland, Ohio.  After completing his Ph.D. in 2006, he started post-doctoral work at the University of Cambridge studying the biomechanics and neural control of invertebrates.   His corpus of work extends from the extremely slow movements of the feeding motions of gastropods to the extremely fast motions of jumping insects.  Regardless of the speed of the motion, he has found that analysis of the musculature is a critical tool for understanding how an animal's behaviour is controlled.  He combines classical mechanics with neurophysiological techniques to determine how interactions between the nervous system, the skeleton, and the musculature result in the wide variety of behaviours we see around us.   He is currently at the University of Bristol studying how bees detect and react to electric fields.

  

Energy storage and release (composite bows)

The first of these problems is a question of power. Muscles simply cannot generate mechanical work quickly enough to accelerate an insect: muscle can generate power at a maximum rate of 150 Watts per kilogram of muscle [Ref. 7]. Jumping planthoppers, however, manage to generate 30,000 Watts per kilogram of their muscles, two orders of magnitude higher than what muscles can do alone (Figure 1). To do this, they use ‘cuticular springs’ as power amplifiers, which the insect uses in the same way a human being uses a bow to shoot an arrow [Refs. 3-5]. The bow generates no energy itself but as we pull back the string, all of the mechanical energy is slowly generated by muscles and stored in the deformation of the wood. When the string is released, recoil of the wood releases the energy extremely quickly, acting as a power amplifier. Insects act similarly using a ‘bow’ made of their cuticle. Prior to a jump, the muscles slowly load this ‘bow’, and then, recoil of the cuticular bow shoots the animal through the air, amplifying the muscle power by orders of magnitude [Refs. 3-5, 8-10]. 

   

Fig 1:  The power requirements for the jumps of various insects. The vast majority of jumping insects require an order of magnitude more powerful to jump than can be generated by muscle alone. Consequently, the insect jump requires a system to amplify power.

 

Until recently, it was thought that insects used two kinds of bow-like energy storage structures: one in the leg of the grasshopper, called the ‘semi-lunar process’, which was made of hardened insect cuticle [Ref. 4], and one in the body of the flea, called the ‘pleural arch’ [Ref. 3], which was made of an extremely energy efficient springy protein called ‘resilin’. Each structure was thought to store energy in a different material. This left the open question of ‘which design is better’, i.e. does the planthopper, the fastest of the insect jumpers, use a ‘grasshopper’ design made of hardened cuticle, or does it use a ‘flea’ design made of springy protein? As is often the case in science, the answer to this question was ‘both’. Planthoppers have an inner layer of springy protein and an outer layer of hardened cuticle (Fig 2, [Ref. 9]).  The layering of hardened cuticle with springy protein, in the same way that a composite bow takes advantage of the mechanical properties of wood and horn, creates a combination that is superior to both [Ref. 9]. 

  

Fig 2: The energy storage ‘bows’ of planthoppers (left) and grasshoppers (right). Both energy storage structures are arches with an outside layer of hardened cuticle (black) with an inside layer of resilin (blue). The composite structure of these energy storage systems allows the insect to take advantage of the different material properties of both materials.

This discovery prompted a re-evaluation of the springs within the flea and the grasshopper – were they really that different? Re-evaluation of the energy storage ‘bows’ within the flea and the grasshopper revealed that the two structures were not that different at all. Both of them used a composite structure made of an inner layer of resilin and an outer layer of hard cuticle [Refs. 8,10]. Thus, there is a general principle that the energy storage mechanism of jumping insects mimics a composite bow [Refs. 8-10].

Directing the energy (mechanical linkages)

Stored energy must be precisely released. Jumping insects do this by having their legs act as mechanical linkage systems which direct the force from the recoiling ‘bow’ to the ground. Depending on the location of the energy storage device, this is done differently. Grasshoppers, which have their energy storage devices in their legs, use their ‘hip’ (also known as the coxa/body joint) to direct jumps. Rotations of the coxa/body joint change the direction of force, allowing the grasshopper to quickly and easily direct a jump or a kick [Refs. 11, 12]. The ease of this directional change allows grasshoppers to change the direction of their jump even in the milliseconds just prior to the recoil of the spring, making it difficult for predators to predict which way the insect will go [Ref. 11]. 

Planthoppers, which have their energy storage device in their body, use a different part of their leg to direct a jump: small muscles in their ‘knee’ (also known as the femur/tibia joint). These muscles can direct the forces from the recoil to the left or the right, similar to the way the grasshoppers use the coxa/body joint to direct the forces when they jump; i.e. both insects use one leg joint as a ‘powered’ joint, and another as a ‘directional’ joint. 

Fleas, in contrast, have a jumping mechanism that combines the leg geometry of the grasshopper with the mechanical energy storage device of the planthopper - with the combined system being extremely difficult to control [Ref. 10]. Strangely, fleas handle this by always jumping in the same direction, with very little variation in the trajectory between individual jumps [Ref. 10].

Synchronizing the legs (gears)    

Of the three most famous jumping insects, planthoppers have a problem fleas and grasshoppers do not: to generate a controlled jump planthoppers require legs which extend almost perfectly synchronously. If planthopper legs do not extend at exactly the same time, the insect will spin wildly out of control [Ref. 13]. Adult planthoppers solve this problem quite simply, by having a frictional contact between their two ‘hips’ which ensures simultaneous extension of the two legs [Ref. 14]. The nymphs, however, have a different and much more spectacular solution. The nymphs have bumps and grooves on each leg, which interlock like a set of modern gears. Prior to a jump, engaging these gears ensures that each leg extends perfectly synchronously [Figure 3, Ref. 15]. These gears represent the very first intermeshing rotating gears that have been discovered in nature, and thus are an evolutionary prototype of high speed - high precision gears for modern machinery. 

  

Fig 3: The leg synchronization mechanism of the nymph planthopper, issus. The nymph has intermeshing gears on the left and right hind legs. Prior to the jump, the insect engages these gears, which ensure that both legs extend at exactly the same time.   

In conclusion 

Composite bows, mechanical linkage systems, and gear trains are all critical to the behavioural success of jumping insects. These biological systems are not just metaphorically similar to the mechanical devices used in modern engineering; they represent designs for precise, targeted, and amazingly fast-moving devices. They are beautiful examples of biomechanics providing elegant solutions for problems that have fascinated mankind for thousands of years.    

By former HFSP Cross-Disciplinary Fellow Gregory Sutton

 

References (* references funded by the HFSP)

[1] The Clouds, Aristophanes, from ‘Lysistrata and Other Plays’, Penguin Books (1973).  Penguin Books Ltd., London.  Translation by Alan H. Sommerstein. 

[2] The Jumper, Hans Christian Andersen, from ‘The Complete Hans Christian Andersen Fairy Tales’, Ambelside Online.  Story 12.

[3] Rothschild M., Schlein J., Parker K., and Sternberg S. (1972).  The jump of the oriental rat flea, Xenospylla cheopis (Roths.).  Nature 239, 45-47.

[4] Bennet-Clark H.C., and Lucey E.C.A. (1967). The jump of the flea: a study of the energetics and a model of the mechanism.  J. Exp. Biol. 47, 59-76.

[5] Bennet-Clark H.C. (1975).  The energetics of the jump of the locust Schistocerca gregaria.  J. Exp. Biol. 63, 53-83. 

[6] Burrows M (2009).  Jumping performance of planthoppers (Hemiptera, Issidae).  J. Exp. Biol. 212, 2844-2855.

[7] Askew G.N. and Marsh R.L. (2002).  Muscle designed for maximum short-term power output: quail flight muscle.  J. Exp. Biol. 205, 2153-2160.

*[8] Burrows M., and Sutton G.P. (2012). Locusts use a composite of resilin and hard cuticle as an energy store for jumping and kicking.  J. Exp. Biol. 215, 3501-3512.

*[9] Burrows M., Shaw S.R., and Sutton G.P. (2008).  Resilin and chitinous cuticle form a composite structure for energy storage in jumping by froghopper insects.  BMC Biology Volume 6, Article 41.

*[10] Sutton G.P. and Burrows M. (2011).  The biomechanics of the jump of the flea, J. Exp Biol. 214, 836-847.

*[11] Sutton G.P. and Burrows M. (2008). The mechanics of elevation control in locust jumping.  J. Comp. Phys. A. 194, 557-563.

*[12] Bayley T.G., Sutton G.P., and Burrows M. (2012).  A buckling region in locust hindlegs absorbs energy when jumping or kicking.  J Exp Biol. 2012 Apr 1;215(Pt 7):1151-61.

*[13] Sutton G.P. and Burrows M. (2010). The mechanics of azimuth control in jumping by froghopper insects.  J. Exp. Biol., 213, 1406-1416.

[14] Burrows M. (2010). Energy storage and synchronization of hind leg movements during jumping in planthopper insects (Hemiptera, Issidae).  J. Exp. Biol., 213, 469-478.

*[15] Burrows M. and Sutton G.P. (2013).  Interacting gears synchronise propulsive leg movements in a jumping insect.  Science, 341, 1254 – 1256.