news and views

Walking speed (m s–1)

Earth Callisto Europa Mars Mercury Saturn Venus Neptune Moon Uranus Io

Jupiter

2.0 1.5 Optimal speed Fr = 0.25

1.0 Fr = 0.50 Walk-run transition

0.5

0

25

50 75 100 125 150 225 Percentage of terrestrial gravity

Figure 1 Walking speed as a function of gravity. The curves represent the predictions of the theory of dynamic similarity. These predictions were made using the Froude-number equation, Fr4v2/(g2l), where v is the velocity in m s11, g is the acceleration due to gravity in m s12, l is 0.92 m (the average leg length for adult male humans), and Fr is 0.25 (which sets the optimal walking speed on Earth9–12) or 0.5 (at which humans move spontaneously from a walk to a run on Earth3). Squares and orange circles refer to measurements of optimal walking speeds4 and walk-to-run-transition speeds5, respectively, in simulated low-gravity conditions. The triangle represents a previous estimate of reduced walking speed on the Moon13. Green circles represent recent measurements of optimal speed obtained using parabolic flight to simulate low- and high-gravity conditions6,7.

similarity also predicts that the lower the gravity, the slower the equivalent walking speed, which depends on the square root of the gravity ratio — the gravity of the planet in question divided by that of the Earth. On Earth, the optimal walking speed and walkto-run-transition speed for an adult man of average height are, respectively, about 1.5 and 2.0 m s11. Figure 1 shows the relationships between walking speed and gravity at Froude numbers of 0.25 (which determines the optimal walking speed for humans) and 0.5 (which determines the walk-to-runtransition speed). One can use the Froude number to predict that the corresponding speeds on a stellar body with 16% of the Earth’s gravity, such as the Moon, will be about 40% (the square root of 16%) of those on Earth — that is, about 0.6 and 0.8 m s11, respectively. These values were also predicted on the basis of a different approach about 35 years ago13, and the impossibility of walking at terrestrial speeds on the Moon has been clear to see in debriefings from the Apollo missions14. Moreover, experimental evidence has confirmed the predictive power of the Froude number in low gravity. Different low-gravity conditions have been simulated NATURE | VOL 409 | 25 JANUARY 2001 | www.nature.com

in the lab by applying a nearly constant upward force to the waist of subjects walking on a motorized treadmill4,5. As predicted, the optimal walking speed4 and the spontaneous transition between walking and running5 occurred at Froude numbers close to 0.25 and 0.5, respectively. The slight discrepancy observed at low gravity (Fig. 1) is likely to be caused by the approximate nature of the simulation — limbs were allowed to swing normally, as if still affected by terrestrial gravity. Cavagna et al.7 now go further, to look at the mechanics of human walking in both low and high gravity. The low-gravity conditions correspond to those on Mars, being 40% of the Earth value. The high-gravity value was 150% of that on Earth. The authors used given portions of the parabolic trajectory of an aeroplane equipped with platforms that were sensitive to forces in all directions. In this way, Cavagna et al. measured the displacement of the body’s centre of mass during a couple of walking steps at different constant gravities and walking speeds. From these measurements, they calculated the recovery of energy. They also recorded the speeds at which energy recovery was optimal (the optimal walking speeds). These speeds closely match those predicted when the Froude number is 0.25 (ref. 15), although the range of optimal speeds in high gravity is quite broad. Indeed, Cavagna et al. conclude that increased gravity increases the range of walking speeds. This is again predicted by the Froude number, as seen in Fig. 1, where the vertical distance between the curves increases with increasing gravity. Here, the vertical distance represents the range of speeds within two dynamically different conditions.

Bipedal and quadrupedal walking — unlike swinging — remain an approximation of ideal pendulum dynamics. Despite this, the Froude number, and the underlying theory of dynamic similarity, has so far proved a handy rule-of-thumb for predicting equivalent walking speeds as a function of body size or gravity. It is not yet known to what extent faster walking speeds can be maintained in high gravity for more than the few steps studied by Cavagna et al.7. But it is nonetheless impressive that an idea introduced in the nineteenth century to produce model ships can be used in the twenty-first century to predict how humans would walk on other planets. ■ Alberto E. Minetti is in the Department of Exercise and Sport Science, Manchester Metropolitan University, Hassall Road, Alsager ST7 2HL, UK. e-mail: [email protected] 1. Thompson, D. W. On Growth and Form (Cambridge Univ. Press, 1961). 2. Alexander, R. M. Nature 261, 129–130 (1976). 3. Alexander, R. M. Physiol. Rev. 69, 1199–1227 (1989). 4. Griffin, T. M., Tolani, N. A. & Kram, R. J. Appl. Physiol. 86, 383–390 (1999). 5. Kram, R., Domingo, A. & Ferris, D. J. Exp. Biol. 200, 821–826 (1997). 6. Cavagna, G., Willems, P. A. & Heglund, N. C. Nature 393, 636 (1998). 7. Cavagna, G., Willems, P. A. & Heglund, N. C. J. Physiol. (Lond.) 528, 657–668 (2000). 8. Cheng, Y. H., Bertram J. E. & Lee, D. V. Am. J. Phys. Anthropol. 113, 201–216 (2000). 9. Cavagna, G. P., Franzetti, P. & Fuchimoto, T. J. Physiol. (Lond.) 343, 232–339 (1983). 10. Dejaeger, D., Willems, P. A. & Heglund, N. C. Pflügers Arch. Eur. J. Physiol 441, 538–543 (2001). 11. Minetti, A. E., Ardigò, L. P., Saibene, F., Ferrero, S. & Sartorio, A. Eur. J. Endocr. 142, 35–41 (2000). 12. Minetti, A. E. et al. Eur. J. Appl. Physiol. 68, 285–290 (1994). 13. Margaria, R. & Cavagna, G. Aerospace Med. 35, 1140–1146 (1964). 14. Minetti, A. E. Proc. R. Soc.Lond. B 265, 1227–1235 (1998). 15. Minetti, A. E. Acta Astron. (in the press).

Plant biology

Floral quartets Günter Theißen and Heinz Saedler Goethe was right when he proposed that flowers are modified leaves. It seems that four genes involved in plant development must be expressed together to turn leaves into floral organs. hat controls the difference between a plant’s floral organs and its leaves? Over 200 years ago Johann Wolfgang von Goethe proposed that the different parts of a plant result from ‘metamorphosis’ (meaning transformation) of a basic organ, the ‘ideal leaf ’. But if floral organs are just modified leaves, what are the modifiers? On page 525 of this issue1 Honma and Goto provide the answer in molecular terms. A typical flower consists of four different types of organ arranged in four whorls (Fig. 1, overleaf). There are leaf-like sepals in the outermost whorl; showy petals in the second

W

© 2001 Macmillan Magazines Ltd

whorl; stamens (male reproductive organs) in the third whorl; and carpels (female reproductive organs) in the fourth, innermost whorl. But not all flowers develop properly. In certain mutants the identity of some floral organs is changed, a phenomenon known as homeosis. In the model plants thale cress (Arabidopsis thaliana) and snapdragon (Antirrhinum majus), for example, such homeotic mutants come in three classes, A, B and C. Class A mutants have carpels in the first and stamens in the second whorl; class B mutants have sepals in the second and carpels in the third whorl; and class C 469

news and views

AP3

PI Petal

AP1 SEP

Stamen

?

AG

SEP

SEP

AG

PI

AP3

SEP

AG

Carpel

?

AP1 AP1

Sepal

Figure 1 Flower structure and the ‘quartet model’6 of floral organ specification in Arabidopsis. According to this model, the identity of the different floral organs — sepals, petals, stamens and carpels — is determined by four combinations of floral homeotic proteins known as MADS-box proteins1,5, 8. The protein quartets, which are transcription factors, may operate by binding to the promoter regions of target genes, which they activate or repress as appropriate for the development of the different floral organs. According to the model, two dimers of each tetramer recognize two different DNA sites (termed CArG-boxes, shown here in grey) on the same strand of DNA, which are brought into close proximity by DNA bending. The exact structures of the multimeric complexes of MADS-box proteins controlling the identity of flower organs are still hypothetical; question marks denote components whose identity is especially uncertain. Proteins: AG, AGAMOUS; AP1, APETALA1; AP3, APETALA3; PI, PISTILLATA; SEP, SEPALLATA.

mutants have petals in the third and sepals in the fourth whorl2,3. Organ identity in the other whorls is unchanged. Following genetic analyses of these mutants, simple models were developed to explain how the different floral organs adopt their unique identities during development2,3. The most widely known is the ABC model, in which combinatorial interactions between three classes of floral homeotic genes are affected in the respective mutants. So these genes are termed class A, class B and class C genes, with A specifying sepals, A&B petals, B&C stamens and C carpels3. (Class D genes, specifying ovules, were later added to the ABC model, but they are not considered further here.) The Arabidopsis class A genes are APETALA1 (AP1) and APETALA2 (AP2); the class B genes are APETALA3 (AP3) and PISTILLATA (PI); and the only class C gene is AGAMOUS (AG). Apart from AP2, these genes are all members of the MADSbox family2–4 which encode transcription factors — proteins that recognize specific DNA motifs of other genes and influence their transcription. Combined loss-of-function of class A, B and C genes results in a transformation of all floral organs into leaves, corroborating Goethe’s view that leaves are a developmental ‘ground state’. But expression of the ABC genes throughout a plant does not transform leaves into floral organs, showing that the ABC genes, though necessary, are not sufficient to superimpose floral 470

organ identity on a leaf developmental programme1,5. So, what other mysterious factors are required to specify floral organ identity? A telling clue came just a few months ago with the report5 that all flower organs resembled sepals in mutants where three other MADS-box genes — SEPALLATA1 (SEP1), SEP2 and SEP3 — had lost their function. Together with gene expression data, this finding suggested that the SEP genes represent another class of floral homeotic genes, termed class E genes6, which, together with the class B and C genes, is required for the specification of organ identity in the petal (A&B&E), stamen (B&C&E) and carpel (C&E)5,6. But by what mechanism do these different genes interact? MADS-box proteins bind DNA as dimers, but attempts to explain the interaction between class A, B and C genes by MADS-box protein heterodimerization have failed7. However, there was a twist to the tale with the demonstration8 that some homeotic MADS-box proteins from Antirrhinum form multimeric DNAbinding complexes. Honma and Goto1 now report that Arabidopsis proteins also bind to DNA as multimeric complexes containing the class B proteins AP3 and PI, the class E protein SEP3, and either AP1 (a class A protein) or AG (a class C protein). These are the exact combinations of proteins required to specify petal (A&B&E) or stamen (B&C&E) identity, respectively. The ability of MADS-box proteins to form multimeric © 2001 Macmillan Magazines Ltd

complexes may therefore provide the molecular basis for the combinatorial interaction of the floral homeotic genes. So are the SEP proteins the mysterious factors that, along with the ABC genes, are required to specify floral organ identity? The answer is clearly ‘yes’. In genetically engineered plants that express B&(A or E) genes throughout development, Honma and Goto found that leaves are transformed into petallike organs, and that ubiquitous expression of class B, C and E genes transforms leaves into stamen-like organs. With these findings1,5, improved successors of the ABC model can be developed. An example is the ‘quartet model’ which directly links floral organ identity to the action of four different tetrameric transcription factor complexes composed of MADS-box proteins (Fig. 1; for details, see ref. 6). Goals for the future will be to define the exact structures of these transcriptionfactor complexes inside the living plant cell, to identify the target genes whose transcription is regulated by the binding of the complexes, and to explain the gene specificity of that binding. The results of Honma and Goto1 also promise progress in answering one of the enduring puzzles of botany: the evolutionary origin of the flower9. The identity of floral organs is totally dependent on the activity of the MADS-type floral homeotic genes, so gene duplication and diversification within the MADS-box gene family must have been key processes in flower evolution4. The MADS-type floral homeotic genes can be separated into three different gene clades (sets of genes that share a last common ancestor not shared with any of the other MADS-box genes)4,10. From phylogenetic reconstructions it seems that these clades — including the class B, class C&D and class A&E genes, respectively — were established within a relatively short period of time well before the origin of the flowering plants. But once established, these gene clades have changed very little4,10. Does this unusual pattern of gene evolution reflect the ‘invention’ of heterotetramer formation and subsequent coevolution of the constituents? Were novel specificities in DNA-binding8 and in the regulation of target genes, generated by the establishment of tetramer formation, required for the specification of more sophisticated reproductive organs, such as flowers or cones? Such questions can now be answered by studying the phylogeny, function and interaction of MADS-box proteins in various groups, including non-flowering plants4,9,10. It was prescient of Goethe to recognize floral organs as modified leaves. But is there even more to it? In his novel Die Wahlverwandtschaften (The Elective Affinities), NATURE | VOL 409 | 25 JANUARY 2001 | www.nature.com

news and views Goethe described the rapid establishment of new ways of sexual reproduction when a married couple (a ‘dimer’) decided to live together with another man and women. By inventing this quartet, did Goethe even anticipate the molecular basis of floralorgan specification? ■ Günter Theißen and Heinz Saedler are in the Department of Molecular Plant Genetics, Max Planck Institute for Plant Breeding Research, Carl-von-Linné-Weg 10, D-50829 Köln, Germany. e-mails: [email protected] [email protected]

1. Honma, T. & Goto, K. Nature 409, 525–529 (2001). 2. Schwarz-Sommer, Z., Huijser, P., Nacken, W., Saedler, H. & Sommer, H. Science 250, 931–936 (1990). 3. Coen, E. S. & Meyerowitz, E. M. Nature 353, 31–37 (1991). 4. Theißen, G. et al. Plant Mol. Biol. 42, 115–149 (2000). 5. Pelaz, S., Ditta, G. S., Baumann, E., Wisman, E. & Yanofsky, M. F. Nature 405, 200–203 (2000). 6. Theißen, G. Curr. Opin. Plant Biol. 4, 75–85 (2001). 7. Riechmann, J. L., Krizek, B. A. & Meyerowitz, E. M. Proc. Natl Acad. Sci. USA 93, 4793–4798 (1996). 8. Egea-Cortines, M., Saedler, H. & Sommer, H. EMBO J. 18, 5370–5379 (1999). 9. Crepet, W. L. Proc. Natl Acad. Sci. USA 97, 12939–12941 (2000). 10. Purugganan, M. D. Bioessays 20, 700–711 (1998).

Quantum physics

Watching an atom tunnel Ali Yazdani Physicists have managed to watch individual hydrogen atoms move on metal surfaces at very low temperatures — in defiance of classical physics. uantum theory, which has just celebrated its 100th birthday, allows particles to break the rules of classical physics. Although, in a classical sense, a particle may not have sufficient energy to cross |a given barrier, quantum theory says that there is still a definite probability that it can penetrate the barrier in a process known as quantum tunnelling. This process is at the heart of many phenomena — from the formation of chemical bonds to what distinguishes a metal from an insulator. Writing in Physical Review Letters, Lauhon and Ho1 report that they have tracked and visualized the quantum tunnelling of individual atoms for the first time. By using a scanning tunnelling microscope (STM), the researchers were able to monitor the motion of individual hydrogen atoms on a metal surface. They found that the atoms remain mobile down to temperatures as low as 9 K. Classically, thermal diffusion or motion is expected to fade away as

a

b

Energy

WILSON HO

Q

the temperature is lowered. But the constant movement of hydrogen implies that there is a quantum effect that allows the atoms to tunnel along the metal’s surface. Quantum tunnelling of atoms at low temperatures has been inferred from experiments on relatively large groups of atoms, but never before has quantum motion been observed so directly — one atom at a time. In condensed-matter physics, quantum tunnelling of atoms is believed to play a key role in phenomena such as the diffusion of impurities in solids and the properties of glasses at low temperatures. An atom typically ‘rests’ in an energy well (Fig. 1a). It can tunnel to another well if it is light enough and if the energy barrier between the wells is sufficiently small. Because hydrogen is so light, it is particularly open to the possibility of quantum tunnelling 2. On the surfaces of metals, the constant movement of hydrogen has been reported down to low temperatures3,4. But whether this

Position

Figure 1 Hydrogen atoms on a copper surface can quantum tunnel at low temperatures. a, A hydrogen atom in an energy well created by the copper surface. The red path shows the energy needed for the atom to diffuse into the next energy well under classical physics. The green path indicates that the atom needs little or no energy to tunnel by quantum mechanical means into the adjacent well. b, An image of a hydrogen atom (dark feature in the centre) on a copper surface taken by scanning tunnelling microscopy. NATURE | VOL 409 | 25 JANUARY 2001 | www.nature.com

© 2001 Macmillan Magazines Ltd

diffusion arises from classical thermal motion or from quantum tunnelling is unclear. Some of the uncertainty can be attributed to the fact that previous experiments measured the average behaviour of a group of atoms, and so could not resolve the role of surface defects in the tunnelling process. A localized probe, such as the tip of an STM, sidesteps these complications. The STM uses the principle of electron tunnelling to give us a close-up view of atoms at surfaces5. A stream of electrons tunnels between a sharp metallic tip and the surface under investigation as the tip skims across the surface. A feedback circuit keeps the flow of electrons constant by adjusting the distance between the tip and the surface. The recorded trajectory of the tip is then used to form an image. The presence of a hydrogen atom on the surface is seen as a dip or ‘hole’ on an STM image (Fig. 1b). This is because an STM image of an isolated atom on a surface depends on how much the atom modifies the surface’s electronic structure. Isolated hydrogen atoms provide very little attraction for the conduction electrons of a metal surface and, as Lauhon and Ho1 show, they appear only as small dips in the STM images of copper at low temperatures (9 K). An identical image is obtained for deuterium, hydrogen’s heavier isotope, because the two are electronically equivalent. But when hydrogen and deuterium are chemically bound to the surface, the STM can distinguish between them because their different masses cause them to vibrate at different frequencies6. The rate at which atoms move across a surface can be measured by making an STM ‘movie’ of the sample. Alternatively, the tip can lock on to an atom and keep constant track of its location. Using both techniques, Lauhon and Ho measured the rate of diffusion of hydrogen and deuterium across a copper surface at different temperatures. From their observations, they ruled out the effect of the STM tip on their measurements. At higher temperatures, they saw both atoms obeying a diffusion law that is consistent with classical motion caused by thermal excitation. But as the surface temperature was lowered, the behaviour of hydrogen and deuterium began to differ dramatically. Deuterium follows classical physics and slows down to a halt. But hydrogen shows a very weak temperature-independent motion, which starts at about 65 K and is still present at 9 K, the lowest temperature used in the experiment. Because hydrogen is much lighter than deuterium, this movement provide strong evidence that quantum tunnelling is at work. A particle’s ability to tunnel is also affected by its immediate environment. For example, lattice vibrations (phonons) and conduction electrons scattering from the atom as 471