NEWS & VIEWS
NATURE|Vol 443|7 September 2006
as black holes5. Typically, Reynolds numbers in
astrophysics are much larger than the values of
a few thousand dealt with by Hof et al.1, indicating a much greater propensity for turbulent
flow. If any turbulence in these astrophysical
flows were transient over long timescales, this
might explain the enhanced accretion and infall rates frequently observed, without the need
to invoke additional instabilities. Such instabilities are generally postulated to be caused
by magnetic fields6,7. Because of the significant
interaction of rotation and turbulence in astrophysical objects, however, we cannot be sure
that Hof and colleagues’ results1 would apply.
From the applied mathematician’s perspective, the implications of these investigations are
fascinating. The motions are best understood
by thinking about a ‘phase space’ of configurations of velocities present in a fluid. In this
depiction, a system evolves in time by moving around the phase space. The laminar state
has a constant velocity field that is smooth and
steady in time. In velocity phase space, this is
represented by a single point, with trajectories
pointing inward from every direction indicating its stability.
For turbulent flow, however, a great tangle of
trajectories would show up some distance from
the laminar point. The turbulent state amounts
to wandering on that tangle, and getting lost
on it for considerable periods of time. If Hof
et al. are correct, however, the system always
— however long it takes — finds a connecting
trajectory that causes it to fall back onto the
laminar attracting point. The exponentially
long times indicate a change in the character
of the turbulent tangle that begs for a deeper
understanding.
The results1 do need to be verified by other
means and in other shear geometries. Previous
studies of the turbulent–laminar transition2,3,
including a study from one of the paper’s
authors2, indicated that the turbulent lifetime
becomes infinite at Reynolds numbers above
around 2,200. This stark contrast between previous and the present results will surely generate considerable activity. The biggest difficulty
here will be that the long lifetimes involved
limit the range of Reynolds numbers that are
practicably testable.
Understanding the idealization of very
smooth walls and a quiet environment will also
require further study. Beyond that, the possibility that these results could be extended to
other shear flows, and the potential for new
turbulence controls, will continue to generate
excitement in this area of research.
■
Daniel Perry Lathrop is in the Departments
of Physics and Geology, and at the Institutes
for Physical Sciences and Technology, and for
Research in Electronics and Applied Physics,
University of Maryland, College Park, Maryland
20742, USA.
e-mail: lathrop@umd.edu
1. Hof, B., Westerweel, J., Schneider, T. M. & Eckhardt, B.
Nature 443, 59–62 (2006).
2. Faisst, H. & Eckhardt, B. J. Fluid Mech. 504, 343–352 (2004).
3. Peixinho, J. & Mullin, T. Phys. Rev. Lett. 96, 094501 (2006).
4. Ott, E., Grebogi, C. & Yorke, J. A. Phys. Rev. Lett. 64,
1196–1199 (1990).
5. Balbus, S. A. & Hawley, J. F. Rev. Mod. Phys. 70, 1–53 (1998).
6. Velikhov, E. P. J. Exp. Theor. Phys. 9, 995 (1959).
7. Sisan, D. R. et al. Phys. Rev. Lett. 93, 114502 (2004).
STRUCTURAL BIOLOGY
Antiviral drugs fit for a purpose
Ming Luo
Did drug researchers have a lucky break when they developed antiviral drugs
for influenza? Crystal structures of enzymes from the H5N1 virus suggest
that they did, and provide avenues for further exploration.
Oseltamivir (Tamiflu) and zanamivir (Relenza)
have been stockpiled by several nations to
counter the threat of a flu pandemic, should the
highly pathogenic avian influenza virus H5N1
develop into a human strain. These drugs are
inhibitors of an enzyme known as neuraminidase, which is found on the surface of the
flu virus. But would these medications hold
their own against a pandemic? Some answers
might be found from the crystal structure of
H5N1 neuraminidases bound to the antiviral
drugs, as reported by Russell et al.1 on page
45 of this issue*. These structures also reveal
a cavity in the active site of certain neuraminidase subtypes that could be exploited to
*This article and the paper concerned1 were published online
on 16 August 2006.
make more effective antiviral drugs.
Avian flu belongs to the genus of influenza
virus known as type A, which is divided into
nine subtypes based on the variety of neuraminidase expressed. The subtypes fall into
two groups2: group-1 contains the subtypes
N1, N4, N5 and N8, whereas group-2 contains the subtypes N2, N3, N6, N7 and N9.
The enzyme facilitates the spread of virus during an infection; oseltamivir and zanamivir
strongly inhibit neuraminidase activity, so
limiting the disease. These inhibitors were
originally developed using crystal structures
of neuraminidase subtypes N9 and N2 and
another neuraminidase from the type B genus
of influenza viruses3–5. The crystal structures,
along with those of neuraminidase–inhibitor
©2006 Nature Publishing Group
a
Group-2
neuraminidase
Active
site
c
Neuraminidase–
inhibitor complex
150-loop
Inhibitor
b
Group-1
neuraminidase
New
cavity
Figure 1 | Induced fit of an enzyme inhibitor. The
influenza neuraminidase enzyme is blocked by
antiviral drugs. Subtypes of the enzyme exist
and are divided into two groups, which differ
in the conformation of their active sites. a, A
loop of amino acids (known as the 150-loop) in
the active sites of group-2 enzyme subtypes is
arranged such that no conformational changes
occur in the active site on binding of an inhibitor.
b, For group-1 subtypes, the 150-loop has a
different conformation from group-2 subtypes,
exposing a large cavity next to it. c, When an
inhibitor binds to group-1 subtypes, the
150-loop adopts a conformation similar to
that of group-2 neuraminidases.
complexes, showed that the three-dimensional
structure of the enzyme active site is the same
for all of these subtypes, and that the inhibitors
bind to the active sites in the same way.
The inhibitors don’t just suppress the activity of the enzyme subtypes that were used to
direct drug development — they have similar
activity against N1 neuraminidase, and are
effective against flu viruses that contain an N1
neuraminidase6. It was always assumed that the
inhibitors bind to the active sites of the group-1
neuraminidases in the same way as for group-2
enzymes, as the amino-acid sequences of the
active sites are essentially the same for all the
subtypes.
However, the crystal structures of the N1, N4
and N8 neuraminidases, reported by Russell
et al.1, surprisingly reveal that the active sites
of these group-1 enzymes have a very different three-dimensional structure from that of
group-2 enzymes. The differences lie in a loop
of amino acids known as the 150-loop, which
has an unexpected conformation that opens up
an adjacent cavity. The 150-loop contains an
amino acid designated Asp 151; the side chain
of this amino acid has a carboxylic acid that, in
group-1 enzymes, points away from the active
site as a result of the ‘open’ conformation of the
150-loop (Fig. 1). The side chain of another
active-site amino acid, Glu 119, also has a
different conformation in group-1 enzymes
compared with group-2 enzymes.
The Asp 151 and Glu 119 amino-acid side
37
NEWS & VIEWS
chains form critical interactions with neuraminidase inhibitors. For neuraminidase subtypes
with the open conformation of the 150-loop, the
side chains of these amino acids might not have
the precise alignment required to bind inhibitors tightly. If so, influenza viruses that contain
these subtypes would be resistant to oseltamivir
and zanamivir. However, the crystal structure
of N1 neuraminidase in a complex with oseltamivir shows that the open polypeptide loop
adopts the conformation observed in the N2
neuraminidase–inhibitor complex. In other
words, when an inhibitor binds, the active site
adopts the conformation seen in the crystal
structures of group-2 enzymes3–5. This ‘induced
fit’ restores the contacts between the amino-acid
side chains of the N1 active site and the inhibitor,
which probably explains why the inhibitors are
effective against N1 influenza viruses.
The difference in the active-site conformation between the two groups of neuraminidases
must be caused by changes to amino acids that
lie outside the active site. This means that an
enzyme inhibitor for one target will not necessarily have the same activity against another
with the same active-site amino acids and the
NATURE|Vol 443|7 September 2006
same overall three-dimensional structure. We
are fortunate that the group-1 influenza virus
neuraminidases assume a tight interaction
with their inhibitors. Otherwise, these antiviral drugs might be ineffective against influenza viruses such as H5N1.
Russell and colleagues’ discovery1 cautions
us to pay more attention to changes in aminoacid sequences outside the active site of
neuramidinases. Such changes might result in
a mutant virus that is resistant to current drugs
if the conformation of the active site is altered
enough to prevent an induced fit of the inhibitors. We must therefore determine the binding
strength of our neuraminidase inhibitors for
each new strain of influenza virus, even if the
amino-acid sequence of the neuraminidase
active site is unchanged compared with that of
existing viruses.
More positively, the cavity near the active site
that is exposed by the open conformation of the
150-loop might be exploited by drug designers.
The affinity of enzyme inhibitors depends on
their fit in their respective active sites. One
could design a chemical group with the right
shape, size and electronic charge to fit snugly
into the newly discovered cavity. Attaching this
group to the scaffolding of existing inhibitors
could then produce a class of neuraminidase
inhibitor that is more effective against H5N1like flu viruses.
When combating pathogenic microorganisms, either bacteria or viruses, we often face
an enemy that continually alters its tactics. The
flu virus is no exception. The way to stay ahead
in this game is to constantly track the changes
of the pathogen and adapt countermeasures
accordingly. The crystal structures reported
by Russell et al.1 provide valuable intelligence
in the war against influenza.
■
Ming Luo is in the Department of Microbiology,
University of Alabama, Birmingham, 1025 18th
Street South, Birmingham, Alabama 35294, USA.
e-mail: mingluo@uab.edu
1. Russell, R. J. et al. Nature 443, 45–49 (2006).
2. Thompson, J. D., Higgins, D. G. & Gibson, T. J. Comput.
Appl. Biosci. 10, 19–29 (1994).
3. Kim, C. U. et al. J. Am. Chem. Soc. 119, 681–690
(1997).
4. von Itzstein, M. et al. Nature 363, 418–423 (1993).
5. Taylor, N. R. et al. J. Med. Chem. 41, 798–807 (1998).
6. Warren, M. K. et al. Antimicrob. Agents Chemother. 46,
1014–1021 (2002).
tion to a quantity describing a phenomenon, we
also have a shot at understanding — in depth,
and beyond a shadow of a doubt — the nature of
the ensuing error term, defined simply as: error
termexact valueour ‘good approximation’.
Barry Mazur
Of course, if our approximation is at all good,
The Sato–Tate conjecture holds that the error term occurring in many major the error term should be small. For many problems, the gold standard of goodness is what we
problems in number theory conforms to a specific probability distribution.
might call square-root accuracy: that the error
That conjecture has now been proved for a large group of cases.
term scales as the square root of the quantity
as it, and the phenomenon it describes, grows
Even under the best circumstances, control- interpretation of questions; mistakes in cod- larger and larger. Great successes in controlling
ling our errors is a dicey business. But as a ing or recoding the data obtained; and other error terms in number theory were achieved in
recent series of mathematical papers1–3 shows, errors of collection, response, coverage and the past century. Specifically, through the work
significant strides are being made — in number estimation4.
of Helmut Hasse5 in the 1930s, André Weil6 in
theory at least. The new work amounts to a
In pure mathematics, however, whenever we the 1940s and Pierre Deligne7 in the 1970s,
proof of a 40-year-old conjecture, known as calculate what we hope is a good approxima- a large class of major approximations were
the Sato–Tate conjecture, for a class of
proved to have this kind of accuracy.
mathematical problems with applicaTake a (randomly chosen) example.
Relative
1 probability
tions in cryptography and the highFor prime numbers p, define N(p) as
speed factorization of large numbers.
the number of ways in which p can
0.75
be written as a sum of 24 squares of
This conjecture predicts the probability distribution of the error terms that
whole numbers. (Squares of positive
0.5
pop up in these problems.
numbers, negative numbers and zero
In any empirical study, errors accuare all allowed.) The ordering of the
0.25
mulate for many reasons. All an experisquares of the numbers that occur in
mentalist can hope for is to know
this summation also counts. Thus,
0.25 0.5 0.75
–1 –0.75 – 0.5 –0.25
1
the sources of most errors, and to be
the first prime number, 2, can already
Scaled error
able to estimate how much trouble
be written as a sum of 24 squares of
they cause.
whole numbers in 1,104 ways, because
distribution of error terms. The Sato–Tate
The web page of the US Bureau of Figure 1 | Probability
there are that many different ways in
2
distribution π √1 − x , the smooth red curve in this figure, can be
Transportation, for example, lists six
which two choices of either (1)2 or
compared with the probability distribution of scaled error terms
possible causes of systematic error in (blue bars) for the number of ways N(p) in which a prime number p
(1)2 can be arranged in a line where
the 1993 US Census count: inability can be written as a sum of 24 square numbers. The data, tabulated
the 22 other numbers are zeros.
to obtain information about all cases for primes p less than a million, agree closely with the distribution,
We know, then, that N(2)1,104.
in the sample; response errors; defi- and give hope that the Sato–Tate conjecture holds for this problem.
What about N(p) for the other prime
nitional difficulties; differences in the (Courtesy of W. Stein; for details of the computation, see ref. 10.)
numbers p3,5,7,11,…? A good
MATHEMATICS
Controlling our errors
38
©2006 Nature Publishing Group