biomechanics serpentine stepsfaculty.washington.edu/fishguy/resources/research... · direction and...

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complex to the vacuole membrane and potentially function as a pore. So de Koning-Ward and colleagues 3 seem to have identified the necessary components for the PTEX that would allow it to function as a gatekeeper. But does the PTEX actually export proteins? The authors show convinc- ingly that it interacts with cargo proteins and, importantly, does so only if the protein carries the export address tag, which is consistent with its proposed function. The PTEX hypothesis is not the only model proposed to explain malaria protein export. Another suggested model 7 is based on the budding of transport vesicles from the vacuole. These vesicles are then predicted to transform into membranous structures in the infected cell known as Maurer’s clefts. It’s possible that different sets of proteins, especially those with different destinies or physical proper- ties, require different machinery to reach their target locations. A third potential model arises from studies on oomycetes. These plant pathogens look like fungi, but are actually evolutionarily related to malaria parasites and also export proteins into the cells of their hosts. Intriguingly, these proteins share the Plasmodium export address tag, and swapping tags between oomycetes and Plasmodium results in export in both cases 8,9 . Oomycete researchers have made two additional observations: they noted that the address tag is also found on host proteins, and that proteins carrying the tag can gain entry to host cells in the absence of the pathogen 10,11 . This might suggest that the pathogens are sub- verting transport elements naturally present in host membranes. Studying mutated versions of any of the central players thought to be involved in these models would provide crucial insights. For instance, deletion of the genes encoding the components of the PTEX complex should ablate protein export and provide conclu- sive proof of the PTEX mechanism. Some of the technical obstacles to generating such mutants in the malaria parasite have recently been removed 12 . The current paper 3 provides a strong mechanistic model of PTEX func- tion and, crucially, identifies a list of excellent candidate genes to be validated in the future. Sarah B. Reiff and Boris Striepen are at the Center for Tropical and Emerging Global Diseases, and the Department of Cellular Biology, University of Georgia, Athens, Georgia 30602, USA. e-mail: [email protected] 1. Scherf, A., Lopez-Rubio, J. J. & Riviere, L. Annu. Rev. Microbiol. 62, 445–470 (2008). 2. Baird, J. K. N. Engl. J. Med. 352, 1565–1577 (2005). 3. de Koning-Ward, T. F. et al. Nature 459, 945–949 (2009). 4. Crabb, B. S. et al. Cell 89, 287–296 (1997). 5. Marti, M. et al. Science 306, 1930–1933 (2004). 6. Hiller, N. L. et al. Science 306, 1934–1937 (2004). 7. Bhattacharjee, S. et al. Blood 111, 2418–2426 (2008). 8. Bhattacharjee, S. et al. PLoS Pathog. 2, e50 (2006). 9. Grouffaud, S. et al. Microbiology 154, 3743–3751 (2008). 10. Birch, P. R. et al. Curr. Opin. Plant Biol. 11, 373–379 (2008). 11. Dou, D. et al. Plant Cell 20, 1930–1947 (2008). 12. Combe, A. et al. Cell Host Microbe 5, 386–396 (2009). The pendular movements of walking are dominated by gravitational forces: the body is pushed up over the planted foot, then falls back down as one foot leaves the ground and the other takes over the load. But as a walk turns to a run, inertia becomes important. Speedy locomotion in limbed animals, from mice to elephants, features this transition to a run, gallop or trot, where mass and velocity drive the animal forward. In the unlikely event that you are chased by a snake and have to run for it, it is natural to sup- pose that the fast-moving snake is similarly exploiting inertial forces. In an article in Proceedings of the National Academy of Sciences, however, David Hu and collaborators 1 present a mathematical model that accu- rately predicts the biomechanics of snake locomotion — they demon- strate that even high-speed slithering is more similar to walking than running, and that it depends heavily on the fric- tional properties of the animal’s scales. Snakes slither on their bellies by bending from side-to-side, propelling themselves forward by pushing with their scales off microscopic bumps, or asperities, in the ground 2,3 . This force, between the scales and the ground, is of course friction; it depends only on the force pushing two surfaces together and their mutual roughness, and is characterized by a coefficient of friction. Crucially, this coefficient depends both on the surfaces involved and on the direc- tion in which that force is applied. From cat tongues to cockleburs, we are all familiar with surfaces that show different coefficients of friction depending on the direction in which they move. Hu and his colleagues 1 show that this phenomenon is central to a snake’s ability to slither swiftly. They modelled a snake as a flexible tube with a uniform cross-section that writhed in a sinusoidal manner. If the frictional coeffi- cients of the belly scales were made equal in all directions, the model snake thrashed about like an eel on a glass table. Clearly the model was flawed, so they moved on to measurements of friction. It is relatively straightforward to meas- ure belly friction in snakes: all that is needed is a board and an anaesthetized snake. In their experiments, Hu et al. placed the snake in various orientations on the board, BIOMECHANICS Serpentine steps Andrew J. Clark and Adam P. Summers Combine theoretical modelling, friction measurements and observations of serpentine slithering. Together, they show that snakes are in effect just taking a walk even when moving at high speed. each time then tilting the board until the snake started sliding. The coefficient of friction is the tangent of the angle made between the ground and the table at which the snake first starts to move. They quickly discovered that, on very smooth boards, snake belly scales have the same frictional coefficient in all directions; but on a board covered with rougher cloth the snake slid more freely forwards than backwards. Most surprisingly, the highest friction occurred when the snake was sliding sideways. Throwing these measured fric- tional values into the wriggling- sausage model yielded a faux snake that moved much like the Pueblan milk snake (Lampropeltis triangulum campbelli, pictured) that the authors used as a reality check. A critical parameter used in the model, called the Froude number, is a dimen- sionless number that appears in many contexts in physics, engi- neering and biology, and that in this instance can be thought of as a ratio of iner- tial to frictional forces. In normal terrestrial locomotion, low Froude numbers are associ- ated with walking and higher numbers with running. In the case of snake slithering, the gravitational or frictional forces are an order of magnitude higher than the inertial forces. So, despite the perception, and even the reality, of high over-the-ground speeds, snakes are not running but walking. The authors also noticed that as snakes slith- ered faster, they lifted the curved parts of their bodies away from the ground as they pushed off the ground with the uncurved parts, all of which is accomplished by redistributing body weight. Modifying the mathematical model to take the body lifting into account, they found an even better predictor of speed. The lifted-snake model was also used for calculating and visualizing the distribution, direction and relative magnitudes of frictional forces along the slithering body. The snake is maximizing its weight in the areas of its body that are subject to a sidewards force. This has the twofold effect of increasing the stability of the pushpoint and decreasing the friction elsewhere on the body. Studies of snake biomechanics have facili- tated the engineering of snake-inspired robots to perform search-and-rescue missions in M. HARVEY/NHPA 919 NATURE|Vol 459|18 June 2009 NEWS & VIEWS © 2009 Macmillan Publishers Limited. All rights reserved

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Page 1: BIOMECHANICS Serpentine stepsfaculty.washington.edu/fishguy/Resources/Research... · direction and relative magnitudes of frictional forces along the slithering body. The snake is

complex to the vacuole membrane and potentially function as a pore.

So de Koning-Ward and colleagues3 seem to have identified the necessary components for the PTEX that would allow it to function as a gatekeeper. But does the PTEX actually export proteins? The authors show convinc-ingly that it interacts with cargo proteins and, importantly, does so only if the protein carries the export address tag, which is consistent with its proposed function.

The PTEX hypothesis is not the only model proposed to explain malaria protein export. Another suggested model7 is based on the budding of transport vesicles from the vacuole. These vesicles are then predicted to transform into membranous structures in the infected cell known as Maurer’s clefts. It’s possible that different sets of proteins, especially those with different destinies or physical proper-ties, require different machinery to reach their target locations.

A third potential model arises from studies on oomycetes. These plant pathogens look like fungi, but are actually evolutionarily related to malaria parasites and also export proteins into the cells of their hosts. Intriguingly, these proteins share the Plasmodium export address tag, and swapping tags between oomycetes and Plasmodium results in export in both cases8,9. Oomycete researchers have made two additional observations: they noted that the address tag is also found on host proteins, and that proteins carrying the tag can gain entry to host cells in the absence of the pathogen10,11. This might suggest that the pathogens are sub-verting transport elements naturally present in host membranes.

Studying mutated versions of any of the central players thought to be involved in these models would provide crucial insights. For instance, deletion of the genes encoding the components of the PTEX complex should ablate protein export and provide conclu-sive proof of the PTEX mechanism. Some of the technical obstacles to generating such mutants in the malaria parasite have recently been removed12. The current paper3 provides a strong mechanistic model of PTEX func-tion and, crucially, identifies a list of excellent candidate genes to be validated in the future. ■

Sarah B. Reiff and Boris Striepen are at the Center

for Tropical and Emerging Global Diseases, and

the Department of Cellular Biology, University of

Georgia, Athens, Georgia 30602, USA.

e-mail: [email protected]

1. Scherf, A., Lopez-Rubio, J. J. & Riviere, L. Annu. Rev.

Microbiol. 62, 445–470 (2008).

2. Baird, J. K. N. Engl. J. Med. 352, 1565–1577 (2005).

3. de Koning-Ward, T. F. et al. Nature 459, 945–949 (2009).

4. Crabb, B. S. et al. Cell 89, 287–296 (1997).

5. Marti, M. et al. Science 306, 1930–1933 (2004).

6. Hiller, N. L. et al. Science 306, 1934–1937 (2004).

7. Bhattacharjee, S. et al. Blood 111, 2418–2426 (2008).

8. Bhattacharjee, S. et al. PLoS Pathog. 2, e50 (2006).

9. Grouffaud, S. et al. Microbiology 154, 3743–3751 (2008).

10. Birch, P. R. et al. Curr. Opin. Plant Biol. 11, 373–379 (2008).

11. Dou, D. et al. Plant Cell 20, 1930–1947 (2008).

12. Combe, A. et al. Cell Host Microbe 5, 386–396 (2009).

The pendular movements of walking are dominated by gravitational forces: the body is pushed up over the planted foot, then falls back down as one foot leaves the ground and the other takes over the load. But as a walk turns to a run, inertia becomes important. Speedy locomotion in limbed animals, from mice to elephants, features this transition to a run, gallop or trot, where mass and velocity drive the animal forward.

In the unlikely event that you are chased by a snake and have to run for it, it is natural to sup-pose that the fast-moving snake is similarly exploiting inertial forces. In an article in Proceedings of the National Academy of Sciences, however, David Hu and collaborators1 present a mathematical model that accu-rately predicts the biomechanics of snake locomotion — they demon-strate that even high-speed slithering is more similar to walking than running, and that it depends heavily on the fric-tional properties of the animal’s scales.

Snakes slither on their bellies by bending from side-to-side, propelling themselves forward by pushing with their scales off microscopic bumps, or asperities, in the ground2,3. This force, between the scales and the ground, is of course friction; it depends only on the force pushing two surfaces together and their mutual roughness, and is characterized by a coefficient of friction. Crucially, this coefficient depends both on the surfaces involved and on the direc-tion in which that force is applied. From cat tongues to cockleburs, we are all familiar with surfaces that show different coefficients of friction depending on the direction in which they move. Hu and his colleagues1 show that this phenomenon is central to a snake’s ability to slither swiftly.

They modelled a snake as a flexible tube with a uniform cross-section that writhed in a sinusoidal manner. If the frictional coeffi-cients of the belly scales were made equal in all directions, the model snake thrashed about like an eel on a glass table. Clearly the model was flawed, so they moved on to measurements of friction. It is relatively straightforward to meas-ure belly friction in snakes: all that is needed is a board and an anaesthetized snake.

In their experiments, Hu et al. placed the snake in various orientations on the board,

BIOMECHANICS

Serpentine steps Andrew J. Clark and Adam P. Summers

Combine theoretical modelling, friction measurements and observations of serpentine slithering. Together, they show that snakes are in effect just taking a walk even when moving at high speed.

each time then tilting the board until the snake started sliding. The coefficient of friction is the tangent of the angle made between the ground and the table at which the snake first starts to move. They quickly discovered that, on very

smooth boards, snake belly scales have the same frictional coefficient in all directions; but on a board covered with rougher cloth the snake slid more freely forwards than

backwards. Most surprisingly, the highest friction occurred when the snake was sliding

sideways. Throwing these measured fric-

tional values into the wriggling-sausage model yielded a faux

snake that moved much like the Pueblan milk snake (Lampropeltis triangulum campbelli, pictured) that the authors used as a reality

check. A critical parameter used in the model, called the

Froude number, is a dimen-sionless number that appears in

many contexts in physics, engi-neering and biology, and that in this

instance can be thought of as a ratio of iner-tial to frictional forces. In normal terrestrial locomotion, low Froude numbers are associ-ated with walking and higher numbers with running. In the case of snake slithering, the gravitational or frictional forces are an order of magnitude higher than the inertial forces. So, despite the perception, and even the reality, of high over-the-ground speeds, snakes are not running but walking.

The authors also noticed that as snakes slith-ered faster, they lifted the curved parts of their bodies away from the ground as they pushed off the ground with the uncurved parts, all of which is accomplished by redistributing body weight. Modifying the mathematical model to take the body lifting into account, they found an even better predictor of speed. The lifted-snake model was also used for calculating and visualizing the distribution, direction and relative magnitudes of frictional forces along the slithering body. The snake is maximizing its weight in the areas of its body that are subject to a sidewards force. This has the twofold effect of increasing the stability of the pushpoint and decreasing the friction elsewhere on the body.

Studies of snake biomechanics have facili-tated the engineering of snake-inspired robots to perform search-and-rescue missions in

M. H

AR

VE

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NH

PA

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NATURE|Vol 459|18 June 2009 NEWS & VIEWS

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Page 2: BIOMECHANICS Serpentine stepsfaculty.washington.edu/fishguy/Resources/Research... · direction and relative magnitudes of frictional forces along the slithering body. The snake is

a

b

Jupiter Io

Satellite spinSatellite

orbital

motion

Jupiter

spin

Io’s tidal

bulge

Jupiter’s

tidal bulge

Satellite

orbital

motion

Perihelion

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Io–Jupiter line

unstable and dangerous environments4,5. Until recently, robots designed for such places all had wheels, which neatly offer huge differences in the friction in the fore-and-aft and side-to-side directions. Hu and colleagues’ investigations1

provide guidance on the types of material that might be used to manufacture a robot belly

that offers similar frictional properties to those of snakes. As a form of locomotion, the slither has a lot going for it. ■

Andrew J. Clark and Adam P. Summers are in

the School of Biological Sciences, University of

California, Irvine, California 92697, USA.

e-mails: [email protected]; [email protected]

1. Hu, D. L., Nirody, J., Scott, T. & Shelley, M. J.

Proc. Natl Acad. Sci. USA doi:10.1073/pnas.0812533106

(2009).

2. Mosauer, W. Science 76, 583–585 (1932).

3. Gray, J. J. Exp. Biol. 23, 101–120 (1946).

4. Guo, Z. V. & Mahadevan, L. Proc. Natl Acad. Sci. USA 105, 3179–3184 (2008).

5. Ostrowski, J. & Burdick, J. in IEEE Int. Conf. Robot. Autom.

1294–1299 (IEEE, 1996).

Jupiter’s moon Io is about the same size as our Moon, but the similarities end there. Its motion around Jupiter is tightly constrained by its gravitational interactions with the giant planet and with two of Jupiter’s other moons, Europa and Ganymede. Io’s orbital imprison-ment is the cause of its spectacular volcanism1.

PLANETARY SCIENCE

Io’s escapeGerald Schubert

According to the latest study, our witnessing of the volcanic splendour of Jupiter’s moon Io might just be a lucky circumstance. The odds are that the satellite will become quiescent on its escape from orbital custody.

Figure 1 | Jupiter–Io tidal interaction. a, The tide raised on Io by its parent planet Jupiter — indicated by the exaggerated elliptical distortion of the body — lags behind the Io–Jupiter line at perihelion (the moon’s orbital point closest to Jupiter) because Io’s orbital rotation is faster than its spin at this position in its orbit. The gravitational torque exerted by Jupiter on Io’s tidal bulge tends to increase Io’s spin at the expense of its orbital energy, and forces Io to move inward. b, The tide raised on Jupiter by Io leads the Io–Jupiter line because Jupiter rotates faster than Io orbits the planet. The Jovian planet’s tidal bulge pulls Io forward in its orbit and, as a result, the moon gains orbital energy and moves outward from Jupiter. Lainey and colleagues2 show that the effect of the tide raised on Io by Jupiter wins out, so Io is moving in towards Jupiter. (Both panels depict the tidal interaction looking from above the orbital plane of Io.)

But Lainey and colleagues2, on page 957 of this issue, provide evidence that Io is loosening the bonds that hold it in its unexpectedly elliptical path around Jupiter. If it eventually breaks free, the most volcanically active object in our Solar System will become dormant.

Io’s intense volcanism is driven by tidal heat

created as Jupiter’s differential gravitational pull causes the satellite to deform continu-ously and repeatedly as it orbits the planet: Io’s surface probably moves up and down by more than 10 metres over an orbit. Jupiter’s varying gravitational pull and the resulting oscillations in the tides on Io occur because the satellite is in an elliptical orbit. If Io were an isolated satellite, tidal heat would circularize its orbit. But Io’s orbit is elliptical, a circumstance dic-tated by the moon’s gravitational interaction with Europa and Ganymede (an interaction referred to as a Laplace resonance). Although Io’s spin and orbital periods still have equal values, Jupiter oscillates back and forth in Io’s sky as Io is alternately closer and more distant from the planet.

It requires energy to tidally deform a body, and part of this energy is eventually dissi-pated as heat by frictional processes within the body. The energy for Io’s tidal heating ulti-mately comes from the energy of Jupiter’s rotation. Figure 1 sketches the gravitational tidal inter action of the planet and its moon. The inter action is two-way, with the planet rais-ing tides on the moon (Fig. 1a) and the moon raising tides on the planet (Fig. 1b). These tides influence the orbital motion of the moon in opposite ways.

The tide raised on Jupiter by Io is carried ahead of the line that connects the two objects — the Io–Jupiter line — because Jupiter spins faster than Io orbits Jupiter. The gravitational attraction of the part of Jupiter’s tidal bulge that is closest to Io pulls Io forward in its orbit, whereas the attraction of the part of the tidal bulge farthest from Io retards the moon’s orbital motion (Fig. 1b). The effect of the part of the bulge closest to Io dominates simply because it is nearer to the moon. As a result, Io gains orbital energy and moves away from Jupiter, whereas Jupiter loses rotational energy. This is the same interaction that is responsible for the Moon receding from Earth as Earth’s rotation rate decreases over time.

However, there is another effect taking place that causes Io to spiral inward towards Jupiter. The planet tidally deforms Io as shown in Fig-ure 1a at the instant that Io passes peri helion (its orbital point closest to Jupiter). The tidal deformation lags behind the Io–Jupiter line because, at perihelion, Io’s orbital rotation is faster than its spin. The gravitational pull on the part of Io’s tidal bulge nearest to Jupiter acts to increase the satellite’s spin to match its orbital rotation. The opposite effect occurs at aphelion (Io’s orbital point farthest from Jupiter), but

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NATURE|Vol 459|18 June 2009NEWS & VIEWS

917-925 News & Views NR IF.indd 920917-925 News & Views NR IF.indd 920 12/6/09 17:15:5612/6/09 17:15:56

© 2009 Macmillan Publishers Limited. All rights reserved