NMR Structure Determination for Larger Proteins Using Backbone-Only Data

Article (PDF Available)inScience 327(5968):1014-8 · February 2010with35 Reads
DOI: 10.1126/science.1183649 · Source: PubMed
Conventional protein structure determination from nuclear magnetic resonance data relies heavily on side-chain proton-to-proton distances. The necessary side-chain resonance assignment, however, is labor intensive and prone to error. Here we show that structures can be accurately determined without nuclear magnetic resonance (NMR) information on the side chains for proteins up to 25 kilodaltons by incorporating backbone chemical shifts, residual dipolar couplings, and amide proton distances into the Rosetta protein structure modeling methodology. These data, which are too sparse for conventional methods, serve only to guide conformational search toward the lowest-energy conformations in the folding landscape; the details of the computed models are determined by the physical chemistry implicit in the Rosetta all-atom energy function. The new method is not hindered by the deuteration required to suppress nuclear relaxation processes for proteins greater than 15 kilodaltons and should enable routine NMR structure determination for larger proteins.
NMR Structure Determination for Larger
Proteins Using Backbone-Only Data
Srivatsan Raman,
* Oliver F. Lange,
* Paolo Rossi,
Michael Tyka,
Xu Wang,
James Aramini,
Gaohua Liu,
Theresa A. Ramelot,
Alexander Eletsky,
Thomas Szyperski,
Michael A. Kennedy,
James Prestegard,
Gaetano T. Montelione,
David Baker
Conventional protein structure determination from nuclear magnetic resonance data relies heavily
on side-chain proton-to-proton distances. The necessary side-chain resonance assignment,
however, is labor intensive and prone to error. Here we show that structures can be accurately
determined without nuclear magnetic resonance (NMR) information on the side chains for
proteins up to 25 kilodaltons by incorporating backbone chemical shifts, residual dipolar
couplings, and amide proton distances into the Rosetta protein structure modeling methodology.
These data, which are too sparse for conventional methods, serve only to guide conformational
search toward the lowest-energy conformations in the folding landscape; the details of the
computed models are determined by the physical chemistry implicit in the Rosetta all-atom
energy function. The new method is not hindered by the deuteration required to suppress
nuclear relaxation processes for proteins greater than 15 kilodaltons and should enable
routine NMR structure determination for larger proteins.
he first step in protein structure deter-
mination by nuclear magnetic resonance
(NMR) is chemical-shift assignment for
the backbone atoms. In contrast to the subse-
quent assignment of the side chains, this process
is now rapid, reliable, and largely automated
(15). Global backbone structural information
complementing the local structure information
provided by backbone chemical-shift assign-
ments (6, 7) can be obtained from H
Overhauser effect spectroscopy (NOESY) , resid-
ual dipolar coupling (RDC) (8), and other (9, 10)
experiments. For lar ger proteins, deuteration be-
comes necessary to circumvent the efficient spin
relaxation properties resulting from their higher
rotational correlation times (11, 12), but remov-
ing protons also eliminates long-range NOESY
information from side chains, except for selec-
tively protonated side-chain moieties (13). The
difficulty in determining accurate structures with
no or limited side-chain information is a major
bottleneck that currently prevents routine appli-
cation of NMR to larger (>15 kD) systems (14).
Here we show that structures of proteins
up to 200 residues (23 kD) can be determined
with the use of information from backbone (H
N, C
,C) NMR data by taking advantage of
the conformational sampling and all-atom ener gy
function in the Rosetta structure prediction meth-
odology (15), which, for small proteins in favor-
able cases, can produce atomic accuracy models
starting from sequence information alone (16, 17).
Structure prediction in Rosetta proceeds in two
steps: (i) a low-resolution exploration phase
using Monte Carlo fragment assembly and a
coarse-grained energy function, and (ii) a com-
putationally expensive refinement phase that
cycles between combinatorial side-chain optimi-
zation and gradient-based minimization of all
torsional degrees of freedom in a physically real-
istic all- atom forc efield (16). The primary obstacle
to Rosetta structure prediction from amino acid
sequence information alone is conformational sam-
pling; native structures almost always have lower
energies than non-native conformatio ns, but they
are very seldom sampled in unbiased trajectories.
Incorporating NMR chemical-shift information
in the selection of the fragments used in the
exploration phase [chemical shift (CS)Rosetta]
(18, 19) provides a robust approach to determin-
ing accurate structures of small (<100-residu e)
proteins using only backbone and
shift data. For larger (>12-kD) proteins, the per-
formance of CS-Rosetta is very target-dependent:
Structures sufficiently close to the native struc-
ture for the energy to drop substantially may be
generated rarely or not at all.
We investigated whether RDC data, which
provide long-range information on the orienta-
tions between bond vectors, can guide the low-
resolution search closer to the native structure
and overcome the sampling problem for larger
(100 to 200 residue) proteins. For every attempted
Monte Carlo move, the alignment tensor is cal-
culated by singular value decomposition (20),
and the decision to accept or reject the confor-
mation is biased by the change in the agreement
between the back-calculated and experimental
couplings (21). Incorporation of RDCs dramati-
cally improved convergence on the correct struc-
ture in a benchmark of 11 a, b,anda/b proteins
ranging in size from 62 to 166 residues (Fig. 1,
Table 1, and fig. S1). As indicated in Table 1, CS-
RDC-Rosetta consistently generates accurate
models for proteins up to 120 resi d u e s and , in
favorable cases, for larger proteins.
For proteins with more than 120 residues,
conformational sampling becomes limiting, even
for the CS-RDC-Rosetta protocol, and the low-
Department of Biochemistry, University of Washington,
Seattle, WA 98195, USA.
Department of Molecular Biol-
ogy and Biochemistry, Center for Advanced Biotechnology
and Medicine, and Northeast Structural Genomics Con-
sortium, Rutgers University, Piscataway, NJ 08854, USA.
Complex Carbohydrate Research Center, University of Geor-
gia, Athens, GA 30602, USA.
Department of Chemistry and
Biochemistry and Northeast Structural Genomics Consortium,
Miami University, Oxford, OH 45056, USA.
Department of
Chemistry, State University of New York at Buffalo, Buffalo,
NY 14260, USA.
Howard Hughes Medical Institute (HHMI) ,
Seattle, WA 98195, USA.
*These authors contributed equally to this work.
Present address: Department of Genetics, Harvard Medi-
cal School, Boston, MA 02115, USA.
To whom correspondence should be addressed. E-mail:
Fig. 1. Impact of RDC
data on conformational
search. Lines depict RMSD
histograms of stru c tu r es
selected in the lowest
10th percentile of coarse-
grained energy for ensem-
bles generated with the
use of CS-Rosetta (black)
or CS-RDC-Rosetta (red). (A)
BcR103A, (B) DvR115G, (C)
RrR43, and (D) SrR115C.
Ang., angstrom.
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energy ensemble is not always close to the native
structure. To further focus sampling, we devel-
oped an iterative refinement protocol that in-
corporates assigned backbone H
Overhauser effects (NOEs) in addition to back-
bone RDCs. As in the previously described
rebuild and refine protocol, a pool of diverse
low-energy conformations is maintained, and the
highest-energy structures in the pool are peri-
odically replaced with offspring (22). The new
protocol, a genetic algorithm, generates hybrid con-
formations by recombining first b-sheet pairings
and, subsequently, fragments of the low-energy
structures (17). T o further enhance sampling, tra-
jectories are seeded with conformations harvested
from previous trajectories that led to low-energy
conformations (23).
The improvement in the model population
with increasing generations in the iterative pro-
tocol is illustrated in Fig. 2 for the 200-residue
ALG13 p rotein using experimentally determined
chemical shift, RDC, and assigned backbone
amide H
NOE data (24). The C
root mean
square deviation (RMSD) to the native structure
and the energy improve from generation to gen-
eration, and after several rounds, discrimination
toward lower RMSD structures is apparent (Fig.
2A, light blue to yellow). After high-resolution
refinement (Fig. 2A, orange to red), the lowest-
energy structures are close to the native structure.
The final low-energy structural ensemble (Fig.
2B) recapitulates the unusual topology in the
previously determined NMR structure (24)(Fig.
2D) to within 3.4 Å RMSD (Table 1). The
Rosetta ensemble fits independent RDC data, as
well as the NMR structure, and the backbone
variation in the ensemble is correlated with back-
bone dynamics as probed by the R1 relaxation rate
(Fig. 2C). The iterative CS-RDC-NOE-Rosetta
models of ALG13 thus appear to be comparable
in quality to the previously published structure
that required substantial effort, including prepara-
tion of selectively methyl- and aromatic-protonated
samples (24).
The iterative CS-RDC-NOE protocol was tested
further on 12 proteins ranging in size from 120 to
266 residues (T a ble 1 and fig. S3). For all proteins
except 1g68, a considerable part of the structure
converges (T able 1). Backbone H
NOE data
were required for convergence of 2z2i, 1i1b, arf1,
2rn2, and 1sua but not for 5pnt, 1s0p, 1f21, and
er553. The RMSDs to the native structures over
the converged regions range from 1.7 to 4.3 Å, with
the exceptions of 1sua and 1f21. For 1f21, high
accuracy (1.6 Å) was reached for a 92-residue
subset (fig. S3). Side-chain accuracy was gener-
ally quite high in the converged regions (fig. S5).
Table 1. Accuracy of models generated with backbone-only NMR data.
Number of
number of
converged in
native over
region (Å)
Depth of
ensemble energy
energy change
resulting from
inclusion of
GmR137 2k5p a/b 62/47 2.6 95.4 32.5¶ 1.8
TR80 2jxt a/b 78/73 1.5 84.9 16.7¶ 0.3
DvR115G# 2kct B 86/66 1.4 80.0 24.3 0.7
LkR15 2k3d a/b 92/74 2.0 85.4 18.0¶ 1.2
BcR103A 2kd1 B 100/65 3.4 61.3 22.7 1.3
SrR115C# 2kcl A 100/95 1.4 86.1 25.1¶ 0.7§§
MaR214A# 2kbn B 102/96 2.1 82.1 43.9 0.6
RrR43 2k0m a/b 104/82 2.1 66.8 12.9 2.9§§
BcR268F# 2k5w A 118/115 1.4 78.4 45.7¶ 1.6
ER553 2k1s a/b 143/115 5.2 46.1§§ 5.1 2.5
ARF1 2k5u a/b 166/141 2.6 73.3 21.6 9.5
AtT7# 2ki8 a/b 122/98 3.0 70.0 37.5 12.5
ER541** 2jyx a/b 124/115 2.5 76.7 31.6 9.9
X-ray** 1f21 a/b 142/122 9.4 76.6 28.5 3.5§§
ER553 2k1s a/b 143/136 1.9 85.2 38.5 15.4
BtR324B** 2kd7 B 150/148 2.4 79.3 51.6 29.1
X-ray** 1i1b B 151/111‡‡ 2.5 71.1 53.3 25.5
X-ray** 1i1b_2†† B 151/133‡‡ 1.7 84.8 100.9 30.5
X-ray** 2rn2 a/b 155/76 3.1 72.9 67.5 24.0
X-ray** 5pnt a/b 157/134 3.0 71.6 34.4 3.0
X-ray** 1s0p A 160/116 4.3 70.8 19.9 10.4
ARF1 2k5u a/b 166/122 2.5 77.2 28.6 8.7
X-ray** 2z2i a/b 179/143 1.8 77.7 46.5 21.6
ALG13 2jzc a/b 201/155‡‡ 3.4 63.7 77.8 12.8
X-ray** 1sua a/b 263/173 6.2 57.0 43.5 26.5
X-ray** 1g68 a/b 266/119 3.2 41.4§§ 36.3 25.1
*NESG codes are used for protein structures obtained with conventional NMR methods in the NESG, and PDB codes for the remaining proteins. The results shown in the top 11 rows were generated with the
CS-RDC-Rosetta protocol and the remaining with the iterative CS-RDC-Rosetta protocol. For the iterative proto col, residues were consi dered converged if they are members of the largest set of
residues that is superimposable within 4 Å. For the noniterative protocol, the residues were selected with the FindCore algorithm (26, 27) based on the conventional NMR ensemble. The global
distance testtotal score (GDT-TS) is the average number of Ca superimposable within 1, 2, 3, 4, and 7 Å, respectively (28). Shown is the median of GDT-TS scores computed for each pair of structures out
of the 10 lowest-energy models. §Energy difference between the median energy of the 10 lowest-energy models and the 10 lowest-energy models that differ by at least 7 Å RMSD from the lowest-
energy model (Rosetta energy units). ||Difference between the median energy of the 10 lowest-energy models obtained with RDC and/or NOE data and the median energy of the 10 lowest-energy CS-
Rosetta models (Rosetta energy units). ¶Energy gap computed with 4 Å cutoff radius (instead of 7 Å). #Blind test case. **Partially or fully synthetic data were used (see table S2). ††All
pairs of H
protons within 5 Å generated an H
NOE distance constraint of 6 Å (17). ‡‡Results are shown with a reduced convergence cutoff of 3 Å (with cutoff 4 Å, 151, 151, and 176 residues
converge and yield a median RMSD of 3.5, 2.3, and 4.9 Å for 1i1b, 1i1b_2, and 2jzc, respectively). §§Violation of validation criterion.
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We carried out a blind test of the new meth-
ods on five data sets generated in the Northeast
Structural Genomics (NESG) Center before con-
ventional NMR structures were determined. For
four of the proteins, the CS-RDC protocol con-
verged (Fig. 3, A to D), whereas for a fifth, con-
vergence was not observed, and blind structure
determination was instead carried out with the
iterative CS-RDC-NOE protocol (Fig. 3E). In
Fig. 2. Determination of ALG13 struc-
ture from backbone NMR data with
Rosetta. (A)RMSDsandenergiesof
structures generated in batches of 2000
during the iterative protocol. Each gen-
eration of structures (color code: blue
to red, corresponds to number of gen-
eration) is based on information from
previous runs (17). Strong convergence
is reached already in the computational
less expensive, low-resolution mode.
The last generations (orange to red)
increase both the precision and accu-
structures within the Rosetta all-atom
energy. The RMSD is computed over
the residues for which convergence
within 3 Å root mean square fluctua-
tions (RMSF) was reached in the 50
lowest-energy Rosetta models (resi-
dues 5 to 70, 81 to 139, 151 to 180).
(B) Ensemble of 10 lowest-energy
Rosetta structures [below line in (A)].
Regions with more than 3 Å RMSF are
depicted in gray. (C)Comparisonof
the RMSF at each residue in the low-
energy Rosetta ensemble to NMR R1
relaxation rate (red, relaxation rates;
black, RMSF in Rosetta ensemble). The relaxation data were not used in the structure calculation. Regions variable in the low-energy structures exhibit increased
dynamics in solution; these data were not used in the structure calculation. (D) NMR solution ensemble based on side-chain NOEs (PDB ID: 2jzc).
Fig. 3. Blind predict i on s w it h t he CS - RD C - Rosetta and iterative CS-
RDC-Rosetta protocols. (Left side of each panel) Superposition
of the 10 lowest-energy predicted structures (red) over the
exp e ri me nt ally solved ensemb l e o f NMR struct u r es ( bl u e ) . (Ri g h t
si d e of each panel) Magnified view of the core side chains.
Rosetta models in (A)to(D) were determined with CS-RDC-
Rosetta, and in (E) with iterative CS-RDC-Rosetta. (A) BcR268F,
(B) DvR115G, (C) MaR214A, (D) SrR115C, and (E) AtT7.
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all five cases (Table 1), the resulting Rosetta-
determined structure is very similar to the con-
ventionally determined NMR solution structure
over both the backbone (Fig. 3, left side of each
panel) and the core side chains (Fig. 3, right side
of each panel), which is notable because no
experimental side-chain information is used in
the Rosetta protocol; the details of core packing
are determined by the Rosetta all-atom energy
function (magnified views of core side chains are
shown for all of the remaining targets in fig. S6).
Thus, our methodology is able to generate
accurate structures of proteins up to ~25 kD from
sparse NMR data without side-chain assignments.
To be useful in practice, it is important that there
be a means of assessing the reliability of the
computed models. Cross-vali dation with inde-
pendently collected data are an excellent way to
do this, but truly independent data may not al-
ways be available, and if the available data are
already sparse, it may not be possible to remove a
subset for independent validation.
Our approach to structure validation is based
on the interplay between the two contributing
sources of structural information: (i) the detailed
physical chemistry implicit in the Rosetta all-
atom energy function and (ii) the experimental
NMR data. As illustrated in Fig. 4A, the all-atom
energy landscape (black) is rugged with many
local minima, making optimization difficult. The
experimental bias based on backbone NMR data
(red), though smoother , is degenerate and lacks
resolution. Because the constrained minimization
of a function will almost always result in higher
function values than unconstrained minimization,
NMR dataconstrained optimization, in general,
should result in higher-energy structures than
bias-free optimization (arrow 1 in Fig. 4A). This
scenario may hold for traditional structure deter-
mination in which the search is almost completely
driven by the experimental data. However , if the
two sources of information are in concordance,
the bias from the experimental data can have two
favorable effects (Fig. 4B). First, optimization far
from the native minimum is impeded, resulting
in an upward shift of the energy of non-native
structures (arrow 1), and second, optimization nea r
the native minimum is improved as the data guide
the search toward the global minimum (Fig. 4, A
and B, arrow 2).
Better optimization in the presence of exper-
imental data (Fig. 4B) is unlikely to occur if there
is no sampling near the correct structure, as data
and the energy function will almost never in-
dependently favor the same incorrect structure.
Hence, we propose the following three criteria
for evaluating the reliability of a calculated struc-
ture (T able 1, columns 6 to 8). First, the calculation
should converge: The lowest-energy conforma-
tions should be very similar to each other over
a large fraction of the structure. For both the
CS-RDC-Rosetta and the iterative protocol,
whenever the calculation converged for more
than 60% of the structure, the RMSD to native
over this region was less than 4 Å (Table 1,
column 6). Second, the converged structures
should clearly be lower in energy than all sig-
nificant ly differen t (RMSD > 7 Å) structures; this
was true for nearly all of our test cases (Table 1,
column 7). Third, the structures generated with
experimental data should be at least as low in
energy as those generated without experimental
data; for none of the successful calculations does
the energy increase significantly when the ex-
perimental data are included in the optimization
(Table 1, column 8). For larger proteins (>120
residues), the data in fact guide the trajectories to
lower-energy structures than those obtained by
unconstrained optimization (Fig. 4D and Table 1,
column 8). As argued above, this is a strong in-
dicator that the correct structure has been found.
When all three criteria were satisfied for the
20 proteins in our test set, the low-energy en-
semble resembles the independently determined
structures. Importantly, the clear structure calcu-
lation failure, 1f21, which converged to a wrong
conformation with an RMSD of 9.4 Å to the
native, fails the third criterion: The energy is higher
ra t he r than lower when the experimental data are
included in the optimization (Fig. 4C and Table
1, column 8). Because we had only one such
failure, we simulated additional failures by de-
leting all near-native structures from the model
populations and computed the three metrics de-
scribed above for these fake minima, (table S1)
(17). For almost all of the proteins, these con-
structed pathological cases again fail the third
Fig. 4. Effect of incorporation of experimental data on energy minimization. (A) The Rosetta all-atom
energy (black line) has many local minima, making minimization difficult, but the global minimum is
generally close to the native structure (N). The experimental bias (red line), though smoother, has de-
generacies and lacks resolution because the data are sparse. Local minima of the all-atom energy and the
experimental bias are uncorrelated far away from the native structure but coincide close to the native
structure. Accordingly, far from the global minimum, including the experimental data during optimization
usually results in higher energies (arrow 1), whereas close to the native structure (N), including the data
results in lower energies (arrow 2). (B) Lines represent the lowest energies sampled by structures at various
RMSDs after optimization in the absence (black line) or presence (red line) of experimental data. Gener-
ally, the all-atom energy and experimental data are in concordance for conformations close to the native
protein structure but not for conformations far from the native structure. If this concordance condition is
met, the experimental data can guide sampling toward the global minimum close to the native structure
(arrow 2), and thus, constrained optimization can result in lower-energy conformations than unconstrained
optimization, whereas biased optimization is less effective than unconstrained optimization distant from
the native structure leading to higher energies (arrow 1). (C and D) In contrast, all-atom energy and RMSD
of final Rosetta ensemble from iterative refinement, with and without experimental data, are shown. Lines
represent the median of the 10 lowest-energy models per RMSD bin. (C) 1f21, an unsuccessful calculation.
Biased optimization with RDC data (red) yields similar energies as unbiased optimization (black); there
is a large remaining energy gap to the native structure (blue dots). (D) Alg13, a successful calculation.
Biased optimization with the experimental data (red) results in lower energies than unbiased optimi-
zation (black).
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criterion: They have higher energies in the ex-
perimentally biased optimization.
For the proteins in our set in the ~30-k D
molecular-weight range, the computed structures
are not completely converged and have large dis-
ordered regions. This is clearly a sampling prob-
lem because the native structure has lower energy
(Fig. 4C and fig. S3); even with the NMR data as
a guide, Rosetta trajectories fail to sample very
close to the native state. Increased convergence
on the low-energy native state can be achieved
either by collecting and using additional experi-
mental data (1ilb_2 in fig. S3) or by improved
sampling. Though at present the former is the
more reliable solution, the latter will probably
become increasingly competitive as the cost of
computing decreases and conformational search
algorithms improve.
We have shown that accurate structures can
be computed for a wide range of proteins using
backbone-only NMR data. These results suggest
a change in the traditional NOE-constraintbased
approach to NMR structure determination (fig.
S4). In the new approach, the bottlenecks of
side-chain chemical-shift assignment and NOESY
assignment are eliminated, and instead, more ba ck-
bone information is collected: RDCs in one or more
media and a small number of unambiguous H
constraints from three- or four-di m e n sion a l
experiments, which restrict possible b-strand regis-
ters. Advantages of the approac h are that
based NOE and RDC data quality is relatively
unaffected in slower tumbling, larger proteins and
that the analysis of resonance and NOESY peak
assignments can be done in a largely automated
fashion with fewer opportunities for error . The
approach is compatible with deuteration neces-
sary for proteins greater than 15 kD and, for
larger proteins, can be extended to include
methyl NOEs on selectively protonated samples.
The method should also enable a more complete
structural characterization of transiently popu-
lated states (25) for which the available data are
generally quite sparse.
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and Experiment Award for providing access to the Blue
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We thank Y. Shen and A. Bax for fruitful discussions;
Y. J. Huang and Y. Tang for their contribution during
preliminary studies using sparse NOE constraints with
CS-Rosetta; S. Bansal, H.-w. Lee, and Y. Liu for collection
of RDC data, A. Lemak for providing the Crystallography
and NMR System RDC refinement protocol, and the NESG
consortium for access to other unpublished NMR data
that has facilitated methods development. S.R., O.F.L.,
P.R., G.T.M., and D.B. designed research; S.R. designed
and tested the CS-RDC-Rosetta protocol; O.F.L. designed
and tested the iterative CS-RDC-NOE-Rosetta protocol;
M.T. developed the all-atom refinement protocol; S.R.,
O.F.L. and D.B. designed and performed research for
energy based structure validation; X.W and J.P analyzed
the ALG13 ensemble; J.A, G.L, T.R, A.E, M.K, and T.S
provided blind NMR data sets; and S.R., O.F.L., P.R.,
G.T.M., and D.B. wrote the manuscript. This work was
supported by the Human Frontiers of Science Program
(O.F.L.), NIH grant GM76222 (D.B.), the HHMI,
the National Institutes of General Medical Science
Protein Structure Initiative program grant U54
GM074958 (G.T.M.), and the Research Resource
grant RR005351 (J.P.). M.T. holds a Sir Henry Wellcome
Postdoctoral Fellowship. RDC and Paramagnetic
Relaxation Enhancement data as deposited in the Protein
Data Bank (PDB) with accession code 2jzc.
Supporting Online Material
Materials and Methods
SOM Text
Figs. S1 to S5
Tables S1 to S3
21 October 2009; accepted 14 January 2010
Published online 4 February 2010;
Include this information when citing this paper.
Limits of Predictability in
Human Mobility
Chaoming Song,
Zehui Qu,
Nicholas Blumm,
Albert-László Barabási
A range of applications, from predicting the spread of human and electronic viruses to city
planning and resource management in mobile communications, depend on our ability to foresee
the whereabouts and mobility of individuals, raising a fundamental question: To what degree is
human behavior predictable? Here we explore the limits of predictability in human dynamics by
studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of
each individuals trajectory, we find a 93% potential predictability in user mobility across the
whole user base. Despite the significant differences in the travel patterns, we find a remarkable
lack of variability in predictability, which is largely independent of the distance users cover on a
regular basis.
hen it comes to the emerging field of
human dynamics, there is a funda-
mental gap between our intuition and
the current modeling paradigms. Indeed, al-
though we rarely perceive any of our actions to
be random, from the perspective of an outside
observer who is unaware of our motivations and
schedule, our activity pattern can easily appear
random and unpredictable. Therefore, current
models of human activity are fundamentally
stochastic (1) from Erlangsformula(2)usedin
telephony to Lévy-walk models describing hu-
man mobility (37) and their applications in viral
dynamics (810), queuing models capturing hu-
man communication patterns (11 13), and mod-
els capturing body balancing (14)orpanic(15).
Yet the probabilistic nature of the existing mod-
eling framework raises fundamental questions:
What is the role of randomness in human be-
havior and to what degree are individual human
actions predictable? Our goal here is to quantify
Center for Complex Network Research, Departments of Physics,
Biology, and Computer Science, Northeastern University,
Department of Medicine, Harvard
Medical School, and Center for Cancer Systems Biology, Dana-
Farber Cancer Institute, Boston, MA 02115, USA.
School of
Computer Science and Engineering, University of Electric
Science and Technology of China, Chengdu 610054, China.
*To whom correspondence should be addressed. E-mail:
19 FEBRUARY 2010 VOL 327 SCIENCE www.sciencemag.org1018
on March 2, 2010 www.sciencemag.orgDownloaded from
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