50 &

100

YEA

RS A

GO

50 YEARS AGOWe wish to report new findings which demonstrate that the cytoplasm can be removed from an amœba in a state in which it displays continuous and vigorous streaming in vitro for periods as long as an hour ... The streaming of amœba cytoplasm in the absence of the plasmalemma and ectoplasmic tube as structures completely eliminates the sol-gel or ectoplasmic contraction theory ... The results of the present work provide additional evidence that the endoplasm of the amœba is not a structureless sol, but rather a material which is structurally and physiologically organized and capable of carrying on cytoplasmic streaming at the subcellular level. The partial disintegration of cytoplasm dissociated from giant amœbæ into ‘motile units of streaming’ provides evidence … for the fountain zone contraction theory of amœboid movement. Each unit of streaming consists of a U-shaped loop or band of cytoplasm with a bend at which a contraction occurs. The two arms of the loop show a difference of consistency; the contracted or ectoplasmic arm is more rigid. Therefore, when the bend is held stationary and the contraction is propagated in one direction, the cytoplasm of the loop streams through the bend in the opposite direction. From Nature 10 September 1960.

100 YEARS AGOThe photograph of the “Leaning” Tower of Pisa in NATURE of August 4 shows clearly that the top tier is not square with the rest. From a rough alignment with the edge of a postcard, the photograph appears as if the tower was of the order of 25 mm./metre out of plumb when the top tier was put on presumably plumb. Exact measures of this and of other parts of the tower might afford interesting data as to the epochs of the construction of the tower and of the progress of its “leaning.”From Nature 8 September 1910.

for further innovation in animal genetics. It has been shown in mice10 that injecting sperm stem cells into testes assures germline transmis-sion of replaced genes while providing a more streamlined route to making pure mutant ani-mals. Optimizing the sperm stem-cell approach in other species will offer the advantage that it does not require breeding schemes to screen embryo-derived chimaeras for germline transmission. Given the long duration of most species’ reproductive cycles, untold time would thus be saved in producing new strains. ■

F. Kent Hamra is in the Department of Pharmacology, and the Cecil H. and Ida Green Center for Reproductive Biology Sciences,

University of Texas Southwestern Medical Center, Dallas, Texas 75390, USA.e-mail: kent.hamra@utsouthwestern.edu

1. http://nobelprize.org/nobel_prizes/medicine/laureates/2007

2. Geurts, A. M. et al. Science 325, 433 (2009).3. izsvák, Z. et al. Nature Methods 7, 443–445 (2010).4. Tong, C., Li, p., Wu, n. L., Yan, Y. & Ying, Q.-L. Nature 467,

211–213 (2010).5. Buehr, M. et al. Cell 135, 1287–1298 (2008).6. Li, p. et al. Cell 135, 1299–1310 (2008).7. kawamata, M. & ochiya, T. Proc. Natl Acad. Sci. USA 107,

14223–14228 (2010).8. Ying, Q.-L. et al. Nature 453, 519–523 (2008).9. Bibikova, M. et al. Mol. Cell. Biol. 21, 289–297 (2001).10. kanatsu-shinohara, M. et al. Proc. Natl Acad. Sci. USA 103,

8018–8023 (2006).

SYSTEMS BIOLOGY

The cost of feedback control Li sun and Attila Becskei

Noise in biochemical processes can compromise precision in cellular functions. An analysis involving information theory suggests that there is a strict limit to how far noise can be suppressed by feedback.

Simple phenomena provide theoreticians with fertile ground for developing fundamen-tal mathematical formalisms, which are then approximated to provide insight into complex phenomena. Such complexity is a characteristic of cell biochemistry. But it is quite a challenge to simplify a cellular network so as to formulate general conclusions about its operation that are, at the same time, experimentally verifiable.

This challenge is tackled by Lestas et al. on page 174 of this issue1. They provide a theo-retical analysis that establishes the limits to which feedback control can suppress noise in a molecular system. Here, noise is the random fluctuation in molecule abundance. Such fluc-tuations are inevitable when the numbers of a molecule present are low2. For example, many plasmids (self-replicating DNA elements) and messenger RNA molecules have mean copy numbers of around one per cell. The smallest possible increase of copy number, from one to two, corresponds to a dramatic 100% change in concentration. Thus, the feedback control of low concentrations is notoriously difficult, and easily leads to overshooting and random oscillations. Furthermore, slight variations in the feedback control scheme result in mark-edly different efficiencies of noise suppression; noise can even be amplified3. These ambigui-ties have hampered the understanding and design of efficient noise control.

Lestas et al.1 broke their system down into three parts: the target and mediator molecules, and a feedback circuitry of arbitrary complex-ity. Although the theory is general, the focus is on target molecules that are present at low copy numbers owing to their slow production and/or fast decay rates. The target enhances

the production of a mediator, which in turn triggers signalling in a circuitry that feeds back on the target. An analogous breakdown of a system has been successful in other types of system analysis: well-defined input–output modules are separated from the rest of the signalling circuitry, which has to meet only general conditions. Such an approach has been used to analyse the number of distinct, stable concentration values that a signalling circuitry can induce; this is important for assessing how robustly cellular memory can function4.

The stochastic control problem was then recast by Lestas et al.1 in the language of infor-mation theory. Information theory has been frequently applied to find fundamental limits in signal processing, for example limits in reli-able data communication. Within this frame-work, it becomes evident why the efficiency of noise suppression is limited. If information processing is personified by the gods of Greek mythology, Tyche and Hermes would represent the randomly fluctuating target and mediator molecules, respectively; Athena would devise the ingenious control schemes.

As the wise Athena constrains Tyche, the capricious goddess of chance, Tyche’s vigour will wane. In turn, Hermes, the faithful mes-senger, delivers less and less information about her to Athena, so that the wise goddess will lack essential information with which to adjust the control schemes. Back in the cellular world, this means that, as the feedback circuit starts to reduce copy-number fluctuations of the target molecule, the information available about them becomes limited because these fluctuations generate the very signal that is needed for the feedback control to suppress the fluctuations.

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NANOTECHNOLOGY

Holes with an edgeHagan Bayley

Tiny holes have been drilled through individual layers of graphene — atomically thin sheets of carbon — using an electron beam. These nanopores might be useful for the ultrarapid sequencing of single DNA molecules.

The idea that DNA could be sequenced by running a strand through a tiny hole — a nanopore — and reading off the bases by electrical detection was suggested 14 years ago1. Since then, significant progress has been made towards this goal2, provoked by the US National Institutes of Health’s $1,000-genome challenge3. Recent developments in base iden-tification seemed to give the upper hand to protein nanopores. However, three papers4–6

now report that nanopores fabricated from graphene — sheets of carbon only one or a few atoms thick — might have crucial advantages for this application.

Graphene7, a hugely extended aromatic mol-ecule of fused six-membered carbon rings, is a material with extraordinary electrical and mechanical properties. On page 190 of this issue, Garaj et al.4 describe how they used an electron beam to bore holes ranging in diam-eter from 5 to 23 nanometres into graphene one or two layers thick. They then mounted the graphene in a chamber with an aqueous salt solution on each side of the film, and measured the current carried by the salt’s ions when a voltage was applied across electrodes immersed in the solutions. The conductances of the nanopores scaled with their diameters, as expected for pores for which the thickness is much less than the diameter8. On the basis of the conductance values, the authors calcu-lated that the effective insulating thickness of the graphene was only about 0.6 nm. This is much smaller than that of other materials that have been used for DNA analysis — 30 nm for typical silicon nitride pores9, for example, and 10 nm for α-haemolysin protein pores10.

Garaj et al. went on to measure the current carried by a graphene nanopore of diameter

5 nm while double-stranded DNA passed through it. They observed spikes in the cur-rent traces, which denoted current blockades corresponding to the transit of both folded and unfolded DNA. Similar blockades had previ-ously been observed in analogous experiments with silicon nitride pores11. A basic solution of high ionic strength ensured that translocation of only a minority of the DNA molecules was hindered by adherence to the graphene sur-face. Using the mean amplitude of the current blockades, the authors were again able to cal-culate the effective thickness of the graphene film, confirming it to be about 0.6 nm.

The graphene used by Garaj et al.4 was prepared by a process known as chemical vapour deposition (CVD). Writing in Nano Letters, Schneider et al.5 report similar data for the translocation of double-stranded DNA through graphene nanopores, but using films that were made by exfoliation (the removal of graphene sheets from bulk graphite). They say that such films have fewer defects than those made by CVD.

In contrast to Garaj and colleagues’ findings, Schneider and colleagues’ data suggest that the conductance of the pores scales with the square of the pore diameter. This indicates that Sch-neider and colleagues’ film was thicker than expected, perhaps because the authors coated it with 6-mercaptohexanoic acid to prevent DNA sticking to the graphene surface.

A third study of DNA translocation through graphene nanopores, also published in Nano Letters, is reported by Merchant and col-leagues6. They worked with CVD-produced graphene that had a thickness of 3–15 atomic layers (rather than just one or two layers, as used by Garaj et al.4), containing pores 5–10 nm

The theory yields surprisingly simple, experi-mentally verifiable solutions, revealing that the ratio of the mean number of mediator molecules to that of the target molecules is a critical factor in setting the limit of noise suppression. When needed, noise suppression is a costly enterprise: a tenfold reduction in noise is possible only if 10,000 mediator molecules are produced for each target molecule. The cost of reducing variation is large in other realms of biology, as well. For example, the maintenance of constant body temperature in mammals (homeothermy) means that they consume around ten times more energy than do reptiles, which have vary-ing body temperatures. Why spend this extra energy? After all, both types of animal thrive on Earth. The reason is that, because of homeo-thermy, mammals are not limited to being active only within narrow ranges of environmental temperature, a factor that is thought to have favoured their global expansion.

It remains to be seen, however, how widely such expensive negative-feedback loops are used in gene-regulatory networks to suppress fast fluctuations in mediator-molecule abun-dance. So far, several plasmids have been iden-tified that produce mediator molecules at an amazing rate, which can indeed contribute to efficient control of copy numbers.

A second insight gained by Lestas et al.1 counters the idea that optimal function is attained when a network evolves to a sufficient complexity. On the contrary, increasing the number of components in the signalling cir-cuitry introduces more opportunities for exter-nal noise to compromise transmission in the feedback circuitry — which, in our mythical analogy, will leave Athena starved of informa-tion. Taking these conclusions to the extreme, it may not be surprising that some mechanisms for plasmid copy-number control lack indirect signalling circuitries altogether. Such control can then be achieved by permitting replica-tion when there is only a single free copy of the plasmid, and by inhibiting replication when two plasmids bind to each other (pairing of the DNA sequences that initiate replication prevents the replication of both plasmids).

Plasmid fluctuations occur on a fast time-scale. When fluctuations are slow, the uncer-tainty in the signal is reduced — Athena can collect more information and exert more precise control. Even without feedback, bio-chemical reaction networks of appropriate structure can exert absolute concentration con-trol over some of the network components5. When evolutionary gene duplication or slow environmental changes alter gene expression, the concentration of the gene product will be kept constant by such networks. Several bio-chemical and genetic networks may combine fluctuations at fast and at very slow timescales, which in turn must be examined by careful experiments, because networks have very different buffering capacities at fast and slow timescales1,5,6. This may also explain why even a simple negative-feedback loop in a genetic

circuit can efficiently reduce concentration heterogeneities in a cell population7.

It will be interesting to compare the opti-mal network structures suited to suppress either slowly varying, inherited population hetero geneities, or fast fluctuations. Break-ing a system down into a few reaction steps to be examined, while confining the properties of the rest of the signalling network in a gen-eral way, should lead to further insights into the operation of cellular networks. Moreover, knowing the limits of system performance will aid progress in biological engineering. ■

Li Sun and Attila Becskei are at the Institute of

Molecular Life Sciences, University of Zurich, CH-8057 Zurich, Switzerland.e-mail: attila.becskei@imls.uzh.ch

1. Lestas, i., Vinnicombe, G. & paulsson, J. Nature 467, 174–178 (2010).

2. Eldar, A. & Elowitz, M. B. Nature 467, 167–173 (2010).3. Marquez-Lago, T. T. & stelling, J. Biophys. J. 98, 1742–1750

(2010).4. Angeli, D., Ferrell, J. E. Jr & sontag, E. D. Proc. Natl Acad. Sci.

USA 101, 1822–1827 (2004). 5. shinar, G. & Feinberg, M. Science 327, 1389–1391 (2010).6. Austin, D. W. et al. Nature 439, 608–611 (2006).7. nevozhay, D., Adams, R. M., Murphy, k. F., Josić, k. &

Balázsi, G. Proc. Natl Acad. Sci. USA 106, 5123–5128 (2009).

See Review, page 167.

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