24. N. H. Packard et al., Phys. Rev. Lett. 45, 712 (1980).
25. F. A. Ascioti et al., J. Plankton Res. 15, 603 (1993).
26. See supplementary materials on Science Online.
27. K. Josic, Nonlinearity 13, 1321 (2000).
28. B. G. Veilleux, thesis, University of Alberta (1976).
29. R. A. Schwartzlose et al., S. Afr. J. Mar. Sci. 21, 289
(1999).
30. G. I. Murphy, J. D. Isaacs, Species replacement in marine
ecosystems with reference to the California current. Minutes
of Meeting Marine Research Committee 7, 1 (1964).
31. R. Lasker, A. MacCall, in Proceedings of the Joint
Oceanographic Assembly, Halifax, August 1982: General
Symposia (Department of Fisheries and Oceans, Ontario,
1983), pp. 110–120.
come more difficult to justify with increasing rec- to resolve causal networks from their dynamical
ognition that nonlinear dynamics are ubiquitous. behavior has implications for system identification
Apparent relationships among variables can switch and ecosystem-based management, particularly where
spontaneously in nonlinear systems as a result of it is important to know which species interact as a
mirage correlations or a threshold change in re- group and need to be considered together. In re-
gime, and correlation can lead to incorrect and source management, as elsewhere, accurate knowledge
contradictory hypotheses. Growing recognition of of the causal network can be essential for avoiding
the prevalence and importance of nonlinear behavior unforeseen consequences of regulatory actions.
calls for a better criterion for evaluating causation
where experimental manipulation is not possible.
References and Notes
Granger causality addresses Berkeley’s issues
with prediction rather than correlation as the cri-
terion for causation in time series. This idea assumes
that causes can be separated from effects, so that a
variable is identified as causative if prediction skill
declines when that variable is removed. This is pos-
sible in a purely stochastic world and is a powerful
idea for systems that can be studied as independent
pieces; however, it is not defined for all systems, and
in particular not for deterministic dynamic systems
(even noisy ones) where Takens’ theorem applies
(19, 20). To address this, we examine an approach
that exploits nonseparability by using CCM to test
for membership to a common dynamical system.
CCM is not a method competing with GC, but
deals with interdependence often found in ecolog-
ical study where GC is simply not applicable. Thus
it is not surprising that as a further check, the GC
calculations for all the model and real data exam-
ples considered in this work were largely unsuc-
cessful (table S2 and GC calculations S1 to S5).
Although many empirical measures of species
interactions exist (e.g., inferring interaction proxies
from diet matrices), we suggest that causation in-
ferred from time-series information provides a
“bottom-line” picture of interactions that is more
direct than those possible with proxies. The ability
1. G. Berkeley, A Treatise on Principles of Human
Knowledge (1710).
2. M. Casini et al., Proc. Natl. Acad. Sci. U.S.A. 106, 197 (2009).
3. G. Sugihara, R. M. May, Nature 344, 734 (1990).
4. P. A. Dixon, M. J. Milicich, G. Sugihara, Science 283,
1528 (1999).
5. W. A. Brock, C. L. Sayers, J. Monet. Econ. 22, 71 (1988).
6. B. T. Grenfell et al., Nature 394, 674 (1998).
7. A. Mysterud et al., Nature 410, 1096 (2001).
8. C. H. Hsieh, S. M. Glaser, A. J. Lucas, G. Sugihara, Nature
435, 336 (2005).
9. G. I. Bischi, et al., Eds., Nonlinear Dynamics in
Economics, Finance and Social Sciences (Springer,
Berlin, 2010).
10. D. A. S. Patil et al., Mon. Weather Rev. 129, 2116 (2001).
11. T. T. Lo, H. H. Hsu, Atmos. Sci. Lett. 11, 210 (2010).
12. X. Rodo, M. Pascual, G. Fuchs, A. S. G. Faruque, Proc.
Natl. Acad. Sci. U.S.A. 99, 12901 (2002).
13. B. K. Wagner et al., Nat. Biotechnol. 26, 343 (2008).
14. A. L. Lloyd, J. Theor. Biol. 173, 217 (1995).
15. Committee on Major U.S. Oceanographic Research
Programs, National Research Council, Global Ocean
Science: Toward an Integrated Approach (National
Academies Press, Washington, DC, 1999).
16. Y. Chen et al., J. Neurosci. Methods 150, 228 (2006).
17. R. M. May, S. A. Levin, G. Sugihara, Nature 451, 893 (2008).
18. C. W. J. Granger, Econometrica 37, 424 (1969).
19. F. Takens, in Dynamical Systems and Turbulence, D. A. Rand,
L. S. Young, Eds. (Springer-Verlag, New York, 1981), pp. 366–381.
20. E. R. Deyle, G. Sugihara, PLoS ONE 6, e18295 (2011).
21. K. McCann, A. Hastings, G. R. Huxel, Nature 395, 794 (1998).
22. C. H. Hsieh et al., Fish. Oceanogr. 18, 102 (2009).
23. P. A. P. Moran, Aust. J. Zool. 1, 291 (1953).
32. T. R. Baumgartner et al., CCOFI Rep. 33, 24 (1992).
33. L. D. Jacobson, A. D. MacCall, Can. J. Fish. Aquat. Sci.
52, 566 (1995).
34. S. McClatchie et al., Can. J. Fish. Aquat. Sci. 67, 1782
(2010).
Acknowledgments: We thank S. Sandin, L. Kaufman, A. MacCall,
J. Melack, J. Schnute, L. Richards, A. Rosenberg, M. Kumagai,
H. Liu, I. Altman, B. Fissel, S. Glaser, B. Carr, E. Klein, L. Storch,
S. Kealhofer, M. Kogler, and C. Perretti for their comments
and assistance with this work, and P. Sugihara for developing
and producing the initial animations for movies S1 and S2.
Supported by NSF grant DEB-1020372, NSF/NOAA CAMEO Award
NA08OAR4320894, the McQuown Chair in Natural Science,
the Sugihara Family Trust, and Quantitative Advisors (http://
qadvisors.com) (G.S.); National Taiwan University and the National
Science Council of Taiwan (C.H.); NSF graduate research fellowships
(H.Y. and E.D.); and an EPA STAR graduate fellowship (E.D.).
Supplementary Materials
Materials and Methods
Figs. S1 to S5
Tables S1 to S26
Box S1
GC Calculations S1 to S5
References (35–76)
Movies S1 to S3
6 July 2012; accepted 4 September 2012
Published online 20 September 2012;
10.1126/science.1227079
REPORTS
alytic scaffold remains a major challenge (2–5).
One class of strategies has relied on the incor-
poration of non-natural metal cofactors within
a protein scaffold to afford artificial metalloen-
zymes (6–9). The main focus in the area has been
improving the selectivity of the hybrid catalysts,
rather than reaction rates, which are, by and large,
dictated by the first coordination sphere interac-
tions around the metal (10–12). Among the var-
ious cofactor localization strategies (13, 14), the
biotin-(strept)avidin technology has proven ver-
satile: The geometry of the biotin-binding pocket
is ideally suited to accommodate organometallic
moieties, leaving enough room for substrate bind-
ing and activation (15–19).
Biotinylated Rh(III) Complexes in
Engineered Streptavidin for Accelerated
Asymmetric C–H Activation
Todd K. Hyster,1,2 Livia Knörr,2 Thomas R. Ward,2* Tomislav Rovis1*
Enzymes provide an exquisitely tailored chiral environment to foster high catalytic activities and
selectivities, but their native structures are optimized for very specific biochemical transformations.
Designing a protein to accommodate a non-native transition metal complex can broaden the scope of
enzymatic transformations while raising the activity and selectivity of small-molecule catalysis. Here, we
report the creation of a bifunctional artificial metalloenzyme in which a glutamic acid or aspartic acid
residue engineered into streptavidin acts in concert with a docked biotinylated rhodium(III) complex to
enable catalytic asymmetric carbon-hydrogen (C–H) activation. The coupling of benzamides and alkenes
to access dihydroisoquinolones proceeds with up to nearly a 100-fold rate acceleration compared with the
activity of the isolated rhodium complex and enantiomeric ratios as high as 93:7.
1Department of Chemistry, Colorado State University, Fort
Collins, CO 80523, USA. 2Department of Chemistry, Uni-
versity of Basel, Basel CH-4056, Switzerland.
hanks to the advent of genetic engineer- displacing established organometal-catalyzed
ing, enzymes are attracting increasing at- industrial processes (1). However, creating an
*To whom correspondence should be addressed. E-mail:
rovis@lamar.colostate.edu (T.R.); thomas.ward@unibas.ch
T
tention as versatile synthetic tools, even enzyme for an abiotic reaction from a noncat- (T.R.W.)
500