Figure 2 | Chaos in the kicked top. a, In this ‘flattened globe’, the two coloured line segments denote two sets of points on the sphere, each representing the initial angular momenta of two collections of atoms. b, The effect of ten iterations of the kicked-top transformation depicted in Figure 1: the green line segment gets only a bit twisted, whereas the red segment is dramatically stretched and folded onto itself — a hallmark of chaos. c, Many iterations of several starting points, clearly showing regions of stability (onion-like rings) and chaos (a fuzz of dots).

a b c

and was not possible in previous studies of tunnelling5–8. The recovery of the full state also permitted observations of other fingerprints of chaos in a quantum system for the first time, such as the generation of quantum entangle-ment and the sensitivity to perturbations to the parameters of the system, rather than to its initial state9.

Interesting future directions for Jessen and colleagues’ work include a push towards the classical limit, where more distinct quantum states live on the sphere. This is a technically dif-ficult regime, but one in which the fingerprints of chaos can be studied in even more detail, and where the controlled transition from quantum stability to classical chaos may be observed. ■

Daniel A. Steck is in the Oregon Center for Optics

and Department of Physics, University of Oregon,

Eugene, Oregon 97403-1274, USA.

e-mail: dsteck@uoregon.edu

1. Chaudhury, S., Smith, A., Anderson, B. E., Ghose, S. &

Jessen, P. S. Nature 461, 768–771 (2009).

2. Bhattacharya, T., Habib, S. & Jacobs, K. Los Alamos Sci. 27, 110–125 (2002).

3. Berry, M. V. Proc. R. Soc. Lond. A 413, 183–198 (1987).

4. Davis, M. J. & Heller, E. J. J. Chem. Phys. 75, 246–254 (1981).

5. Dembowski, C. et al. Phys. Rev. Lett. 84, 867–870 (2000).

6. Hensinger, W. K. et al. Nature 412, 52–55 (2001).

7. Steck, D. A., Oskay, W. H. & Raizen, M. G. Science 293, 274–278 (2001).

8. Steck, D. A., Oskay, W. H. & Raizen, M. G. Phys. Rev. Lett.

88, 120406 (2002).

9. Peres, A. Quantum Theory: Concepts and Methods (Springer,

1995).

VISION

Gene therapy in colourRobert Shapley

Replacing a missing gene in adult colour-blind monkeys restores normal colour vision. How the new photoreceptor cells produced by this therapy lead to colour vision is a fascinating question.

Colour blindness is a common genetic disorder (affecting about 5–8% of males, although fewer than 1% of females) in which the absence of a single gene on the X chromosome leads to a specific loss of function. Normal human colour vision relies on three distinct photopigments in the retina’s cone photoreceptors. Those who do not inherit the gene for one of the three cone pigments are called dichromats; such individuals cannot distinguish the difference between some pairs of colours that trichro-mats can discriminate easily. John Dalton, the famous British chemist, was a dichromat, and colour blindness is often referred to as daltonism.

Colour blindness is common in New World monkeys, such as the squirrel monkey (Saimiri sciureus), because the species does not have all three of the cone-pigment genes that humans usually have. All male and some female squirrel monkeys are colour-blind dichromats, although

most female squirrel monkeys achieve trichro-matic colour vision. But let’s pay attention to squirrel monkey dichromats. Mancuso et al.1 report in this issue (page 784) that injecting a virus carrying a gene for the missing photo-pigment into the retina of adult colour-blind squirrel monkeys confers normal trichromatic vision; 20 weeks after injection the new pig-ment was expressed in cone photoreceptors and the formerly dichromatic monkeys began to discriminate between two colours that had looked identical to them before treatment. Mancuso and colleagues1 named one of their dichromatic monkeys Dalton after the chemist, but at the end of their experiments their Dalton was no longer colour blind. The success of these experi ments offers promise that, perhaps in the foreseeable future, a similar therapy might improve visual function in humans. At the same time, these results raise a number of interesting questions about colour vision in primates.

it, whereas an atom in an ‘island of stability’ is trapped there, confined to its particular ‘ring’.

But now back to quantum mechanics — we’re talking about atoms, after all. As a conse-quence of Heisenberg’s uncertainty principle, quantum states of atoms can’t be single points on the sphere, but must be smeared out to occupy at least some finite area. And again, there can be no chaos in the quantum case, in stark contrast to the classical model. Tradi-tionally, there have been two approaches to this problem of the missing quantum chaos. One is to study the conditions under which the classi-cal and quantum descriptions agree. For exam-ple, under a weak, continuous measurement, a quantum system can be persuaded to display chaos as appropriate to the classical case2. The other is to study the ‘fingerprints’ of chaos3 in the quantum system, and this is the approach taken by Jessen and collaborators1.

The authors studied a phenomenon called dynamical tunnelling4. This is a bit different from the better-known barrier tunnelling, in which a quantum particle can penetrate a potential barrier despite not having enough energy to hop over it. Recalling the kicked-top behaviour depicted in Figure 2c, notice that there are two main stable islands in the left hemisphere and that a consequence of stabil-ity is that, classically, an atom starting in either island is trapped there — not by any potential barrier, but merely as a consequence of the twist/turn dynamics. Because of the symme-try of these two islands, quantum mechanics allows an atom starting in one island to hop back and forth to the other island, a dynamical tunnelling process between two atomic orien-tations strictly forbidden in the classical world. Jessen and collaborators’ experiments clearly demonstrated this, as well as an atomic quan-tum state sitting placidly in the large island and another moving erratically (though not chaotically) in the chaotic region — carefully respecting the classical boundaries between stability and chaos, despite being far into the quantum regime.

The beauty of the experiments1 lies in the complete reconstruction of the quantum state, leaving no aspect of the tunnelling pro cess hid-den. This is no easy task, involving the process-ing and combination of many measurements,

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In humans, monkeys and most other verte-brates, each cone photoreceptor absorbs light over a broad range of the visible spectrum and transduces it into electrical signals. We identify each cone type by its light-absorb-ing photopigment, which is named for the wavelength of peak absorption. Humans have short-wavelength S-cones (with peak absorption at ~440 nm), medium-wavelength M-cones (peak absorption ~535 nm) and longer-wavelength L-cones (peak absorption ~560 nm). Colour blindness in humans is usually caused by an absence of either M- or L-cones; from his symptoms, we can infer that John Dalton was missing M-cones.

Dichromatic squirrel monkeys have S-cones but only one other cone type — a middle-wave-length cone that contains only one of three pos-sible middle-wavelength pigments (denoted M1, M2 and M3) with peak absorptions at 535, 545 and 560 nm, respectively; M3 in the squir-rel monkey is like the human L-cone pigment, M1 like the human M-cone pigment.

There is no direct connection between the peak absorption wavelength and the role of the cone in colour perception; although L-cones (560 nm) are crucial for our ability to see red, the appearance of 560-nm light is in fact green-ish-yellow. But there is no mystery about this — the signals for colour are not the signals from individual cones but rather the cone-difference signals computed by post-receptoral cells in the retina and in the brain. Signals from the cones are passed through bipolar cells to the retinal ganglion cells which lie in a deeper layer of the retina and transport visual information to

the brain. The retinal ganglion cells that carry signals about colour are called cone-opponent ganglion cells because they subtract the signals from different types of cone photoreceptor2. In most mammals there are ganglion cells that subtract signals from longer-wavelength cones from the excitatory signals from S-cones, and these ganglion cells tell the difference between blue and yellow3. For example, in Old World primates the blue–yellow signal difference is usually computed as S − (L+M). The blue–yellow ganglion-cell pathway in an individual squirrel monkey dichromat can be S − M1, S − M2 or S − M3, depending on what longer-wavelength pigment the monkey has.

Humans and Old World monkeys also have red–green cone-opponent retinal ganglion cells, the responses of which are proportional to the difference between signals from L-cones and M-cones (L − M or M − L). In trichromatic squirrel monkeys there is also a red–green pathway that computes the difference between the two longer-wavelength cones: M3 − M1, M3 − M2, or whatever pair of cones the monkey has4. In Old-World monkeys there are many more red–green than blue–yellow ganglion cells, but in trichromatic squirrel monkeys the blue–yellow ganglion cells are much more numerous than the red–green4.

Dichromatic squirrel monkeys with only M1-cones cannot discriminate blue–green lights with wavelengths of around 495 nm from grey light. But Mancuso and colleagues1 report that, after therapy with the gene encoding the M3 pigment, their treated monkeys can easily tell blue–green from grey, just like trichromats.

One of many open questions to arise from these results is: what type of cone-opponent ganglion cell is active in the treated monkeys?

There are two possibilities (Fig. 1). First, M1-cone signals from cones not affected by virus could be subtracted from the new M3-cone signals, in effect producing a new function-ing red–green (c3M3 + c1M1) – M1 pathway, where c3 and c1 are weighting coefficients ≠1. This possibility would require that M3-cone signals are connected with some specificity to ganglion cells, for instance M3-cone signals would only be excitatory while M1-cone signals could remain both excitatory and inhibitory.

A second possibility is that new M3-cone signals could be subtracted from S-cone signals to produce a new functioning blue–yellow S – (M1 + M3) pathway that would complement the S − M1 pathway already present in the dichromat4. Having both S − M1 and S − (M1 + M3) cells would allow the monkey to discriminate between blue–green and grey.

One outstanding feature of Mancuso and colleagues’ data1 makes the second explana-tion — let’s call it the blue–yellow hypothesis — more plausible. The authors monitored the time course of cone-pigment function after gene therapy by measuring cone signals in an electroretinogram (ERG), and they report that signs of new, functioning M3-cone pig-ment appeared about 20 weeks after injection. Almost simultaneously with the appearance of viable new photopigment, the formerly dichromatic monkeys became able to perform the colour-discrimination task as proficiently as trichromats. That there was no measur-able delay in visual function suggests that the new cone signals were combined immedi-ately in pre-existing colour channels from eye to brain.

The blue–yellow hypothesis would theoreti-cally require little or no rewiring, which is why it seems more likely. But this is only specula-tion. The question can be answered by mak-ing electrophysiological measurements in the treated squirrel monkeys to determine whether or not there are new red–green cone-opponent retinal ganglion cells or red–green cells in the lateral geniculate nucleus2,4 (the first target of retinal ganglion cells), and also whether or not there are new S – M3 or S – (M1 + M3) blue–yellow cells as well as S – M1 cells.

In their paper1, Mancuso et al. remind us of the long-held belief that “neural connections established during development would not appropriately process an input that was not present from birth”, but their results refute this idea. Their paper is a pointer to future exciting research. ■

Robert Shapley is at the Center for Neural Science,

New York University, New York 10003, USA.

e-mail: shapley@cns.nyu.edu

1. Mancuso, K. et al. Nature 461, 784–787 (2009).

2. De Valois, R. L. Cold Spring Harb. Symp. Quant. Biol. 30, 567–579 (1965).

3. Jacobs, G. H. Phil. Trans. R. Soc. B 364, 2957–2967 (2009).

4. Jacobs, G. H. Vision Res. 23, 461–468 (1983).

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Figure 1 | Two paths to colour vision after gene therapy. The figure shows two different schemes that could generate trichromatic vision in populations of a dichromat’s cone-opponent ganglion cells after gene therapy. Excitatory connections between cones and ganglion cells are indicated by white bars and inhibitory connections by black bars. a, The new pigment M3 is inserted into cones that excite ganglion cells that are not cone-opponent and do not respond to colour in the dichromats (left) because they compute differences of M1-cone inputs only. These cells may become M3 − M1 cone-opponent cells after injection (right), producing a functional red–green pathway in treated monkeys. This is a simplified schema; a more realistic connectivity is (M1 + M3) − M1. b, The new pigment M3 can substitute for some M1 pigment and thereby generate S − M3 cells (right) that exist alongside and functionally complement the S − M1 cells that are already present in the dichromat (left). Once again, a more realistic picture would show the treated cells to be S − (M1 + M3).

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