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Transient tertiary structures in tau, an intrinsicallydisordered proteinAnna Battistia, Gabriele Ciascab & Alexander Tenenbaumc

a LISC, FBK-CMM and University of Trento, via Sommarive 18, 38123Povo (TN), Italyb Physics Institute, Catholic University, Largo Francesco Vito 1, 00168Rome, Italyc Physics Department, Sapienza University, Piazzale A. Moro 5, 00185Roma, ItalyPublished online: 11 Jun 2013.

To cite this article: Anna Battisti, Gabriele Ciasca & Alexander Tenenbaum (2013) Transient tertiary structures in tau, anintrinsically disordered protein, Molecular Simulation, 39:13, 1084-1092, DOI: 10.1080/08927022.2013.794275

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Transient tertiary structures in tau, an intrinsically disordered protein

Anna Battistia*, Gabriele Ciascab and Alexander Tenenbaumc

aLISC, FBK-CMM and University of Trento, via Sommarive 18, 38123 Povo (TN), Italy; bPhysics Institute, Catholic University,Largo Francesco Vito 1, 00168 Rome, Italy; cPhysics Department, Sapienza University, Piazzale A. Moro 5, 00185 Roma, Italy

(Received 21 January 2013; final version received 4 April 2013)

An intrinsically disordered protein (IDP) does not have a definite 3D structure, and because of its highly flexible nature itevolves dynamically in very large and diverse regions of the phase space. A standard molecular dynamics run can sampleonly a limited region of the latter; even though this kind of simulation may be effective in sampling local temporarysecondary structures, it is not sufficient to highlight properties that require a larger sampling of the phase space to bedetected, like transient tertiary structures. But if the structure of an IDP is dynamically evolved using metadynamics (analgorithm that keeps track of the regions of the phase space already sampled), the system can be forced to wander in a muchlarger region of the phase space. We have applied this procedure to the simulation of tau, one of the largest totally disorderedproteins. Combining the results of the simulation with small-angle X-ray scattering yields a significant improvement in thesampling of the phase space in comparison with standard molecular dynamics, and provides evidence of extended hairpin-and paperclip-like transient tertiary structures of the molecule. The more persistent tertiary pattern is a hairpin foldingencompassing part of the N-terminal, the proline-rich domain, the former repeat and a functionally relevant part of thesecond repeat.

Keywords: transient tertiary structures; tau protein; intrinsically disordered proteins; metadynamics

1. The tau protein

Intrinsically disordered proteins (IDPs) in their native state

are similar to highly denaturated globular proteins, and

fluctuate between many conformations [1,2]; IDPs entail

at least an extended disordered region but can also entail

globular domains alternating with flexible linkers or

disordered domains.1 These proteins are therefore

characterised by different degrees of disorder, from those

formed by globular domains connected by disordered

segments to those totally disordered, which are similar to a

random coil.[1,2] Even the latter may entail segments

endowed, albeit temporarily, with secondary structures

like a-helices, b-sheets or PPII helices.[3] An open

question is how to characterise their time-dependent

overall tertiary structure.

The tau protein is one of the largest totally disordered

IDPs.[4] It exists in several isoforms2; its htau40 isoform,

found in the human central nervous system, has 441

residues and a molecular weight of 45.85 kDa.

Four domains, corresponding to morphologically

different sections of the htau40 molecule, can be

distinguished in its primary sequence: the N-terminal

projection domain (residues 1–150); a proline-rich

segment (residues 151–243); a domain entailing four

repeats (residues 244–368); the C-terminal domain

(residues 369–441).

Protein tau is involved in the nucleation and

stabilisation of the microtubules (MTs) in the axons of

the neurons. Stabilisation is achieved through the bonding

of the repeats domain of tau to the a- and b-tubulines

forming the MTs.[5] On the other hand, protein tau can

aggregate in paired helical filaments (PHFs) forming

fibrils, which in their turn form insoluble tangles.[1,5] This

pathological deviation from its physiological function

plays a central role in the development of Alzheimer’s

disease.[6] The process of formation of the PHFs is not

entirely known, but some of its factors and stages have

been investigated. A precursor stage of tau polymerisation

has been related to specific transient global folds of the

protein, in which the N-terminal is folded near the repeats

domain in a hairpin conformation,[3,7,8] or the C-terminal

is in the neighbourhood of the repeats domain and the N-

terminal is folded near the C-terminal in a paperclip

conformation. [9–11]

Thus, particular tertiary structures, albeit transient, are

supposed to play a key role in the pathological evolution of

the molecule. These structures are likely to evolve over

times and regions of the phase space that are much larger

than those characteristic of temporary secondary struc-

tures. It is therefore important, to gather information on the

existence and probability of configurations endowed with

statistically significant tertiary structures, to achieve a

dynamical simulation of tau able to sample its overall

structure over large regions of the phase space.

q 2013 Taylor & Francis

*Corresponding author. Email: battistia@libero.it

Molecular Simulation, 2013

Vol. 39, No. 13, 1084–1092, http://dx.doi.org/10.1080/08927022.2013.794275

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2. The dynamical simulation

Given the speed at which transitions between confor-

mations of an IDP are supposed to take place, the

simulation of their dynamics seems to be a promising tool

to understand their behaviour. The dynamical simulation

of an IDP is a computational challenge because by

definition there are no available 3D structures of the whole

molecule from which to start. To overcome this obstacle,

we have described in a previous paper [12] a procedure

that has been proved to be effective in sampling local

temporary secondary structures [13]; but this procedure

would not be effective in sampling larger regions of the

space, as required to detect properties like statistically

relevant, albeit transient, tertiary structures. Metady-

namics is a simulation tool that greatly expands the

exploration of the phase space of an IDP, allowing a

significant sampling of its fluctuating tertiary structure.

In order to perform a dynamical simulation of tau, we

start from its primary sequence of amino acids, as in [12].

We use this sequence as an input of the visual molecular

dynamics (VMD) program [14]; this program lines up the

amino acids following their primary sequence, departing

from a straight line only when obliged by excluded volume

effects due to neighbouring amino acids. The output of

VMD is thus a 3D sequence of straight segments of amino

acids; this structure is immersed in implicit water,[15] and

used to start a simulation at the beginning of which it

rapidly evolves – within 50 ps – to a more natural

conformation. We have used for this simulation the

molecular dynamics (MD) GROMACS package3; the

simulation has been carried out at constant temperature and

pressure and at neutral pH (pH 7), close to the physiological

value (in the 7.2–7.4 range). Accordingly, amino acids

were set to their default protonation states at pH 7, i.e. with

Lys, Arg carrying aþ1 and Glu, Asp a21 net charge. The

dynamic evolution integrates the metadynamics algorithm,

that keeps track of the regions of the phase space already

sampled by the molecule, and forces the system to leave

those regions and to wander in other regions of the phase

space.[16] The system thus samples a portion of the phase

space much larger than the one it would sample in an equal

time of standard MD simulation.

The collective dynamical variable we have chosen to

implement the metadynamics method is the gyration

radius Rg ¼ ðP

i r2i mi=

Pi miÞ

1=2, where ri are the positions

of the atoms with respect to the centre of mass of the

molecule, and mi are their masses; Rg measures the overall

size of a molecule. The Rg of tau has been measured by

small-angle X-ray scattering (SAXS), and on average

Rg ¼ 6:8 nm at T ¼ 300 K.[17] We have fixed the

parameters of the metadynamics algorithm in such a way

that Rg oscillates around its experimental value.4

We have monitored the time evolution of tau by

computing Rg: Figure 1 shows the gyration radius during a

10-ns evolution. The metadynamics algorithm induces

large structural changes in the molecule, with the gyration

radius spanning the range between 2.5 and 11 nm, centred

near the experimental value; its average over this

evolution is Rg ¼ 6:3 nm. The large oscillations of Rg

hint at the variety of configurations sampled by the system

in different regions of the phase space.

The way in which the metadynamics algorithm works

can be better understood by separately computing the time

evolution of the gyration radius of the N-terminal domain,

of the proline-rich segment, of the repeats domain and of

the C-terminal domain. The results are reported in Figure 2

Time (ns)

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10

12

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)

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Figure 1. Time evolution of the radius of gyration of protein tauduring the metadynamics at T ¼ 300 K. The experimentalaverage value of Rg is 6.6 nm.[10]

Time (ns)

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14

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Figure 2. Time evolution of the radius of gyration of fourdomains of tau protein at T ¼ 300 K. Curve 1 (black): residues1–150, N-terminal domain; curve 2 (red): residues 151–243,proline-rich segment; curve 3 (blue): residues 244–368, repeatsdomain; curve 4 (green): residues 369–441, C-terminal domain.

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and show that all four domains undergo very strong

modifications. The algorithm shakes them alternatively,

leaving from time to time one of the domains in what

appears to be a local equilibrium well. So as an example,

the proline-rich domain is almost stable during the first

2 ns, whereas the other domains show strong changes in

their overall configuration; the first domain reaches again a

relative stability between 3.5 and 6.3 ns, and between 9.0

and 9.6 ns. Also the other domains stay for some time in a

quasi-equilibrium state: the C-terminal between 5.2 and

6.3 ns, the N-terminal between 5.8 and 6.8 ns and the

repeats domain between 5.2 and 6.4 ns. The large

amplitude of the oscillations of the N-terminal is due to

its higher flexibility in comparison to the other domains, in

particular the domain entailing the repeats [3].

3. The SAXS experiment

We extract form the data produced by the metadynamics

simulation the most significant sampling of the equili-

brium dynamics of tau by combining them with

experimental SAXS results obtained from a specimen of

tau in solution. The SAXS experiment has been performed

using full-length htau40 purchased from Sigma Aldrich

(product code: T0-576). The powder was reconstituted in

50mM 2-(N-morpholino)ethanesulfonic acid (MES), pH

6.8, 100mM NaCl and 0.5mM ethylene glycol tetraacetic

acid (EGTA) and concentrated at the nominal concen-

tration of 2mg/ml in 0.1 £ phosphate buffer saline (PBS)

solution (ionic strength ,0.02M; 10 £ PBS: 1.3M NaCl,

0.07M Na2HPO4 and 0.03M NaH2PO4, pH 7.4) by the

QuickSpin protein concentration/buffer exchange (Dual-

system Biotech AG, Schlieren, Switzerland). Sub-

sequently, the solution was centrifuged for 10min at

10,000 g and the supernatant passed through a 20-nm pore

size syringe filter to eliminate aggregates. Protein quality

was assayed by SDS-PAGE in 12% (w/v) polyacrylamide,

according to Laemmli.[18] The gels were stained with

Coomassie Brilliant Blue R-250. The SDS-PAGE analysis

revealed the occurrence of a major protein band with the

expected size (,45 kDa), a purity .90% and the absence

of a significant amount of aggregates.

SAXS measurements have been acquired on the

BioSAXS beamline (ID 14-3) at the Synchrotron

Radiation Facility ESRF (Grenoble, France) [19], at a

constant temperature of 303K, for two solute concen-

trations, namely 1 and 2mg/ml. A volume of 50ml of

solution has been placed in a 1.8-mm diameter quartz

capillary with a few tens of micron wall thickness. Data

acquisition has been performed with a PILATUS 1M

detector in the scattering range 0.01–5.8 nm21. Ten 2-s

exposures were compared, without observing any

radiation damage. SAXS data reported in the following

were obtained with an exposure time of 3 s. Solvent

scattering was measured to allow an accurate subtraction

of the background scattering. As reported in [10],

spectrophotometric determination of the tau concentration

in solution is not reliable due to the scarcity in the tau

primary sequence of aromatic residues, which are

responsible for the optical absorption at 280 nm. As a

consequence, the molecular mass of the protein cannot be

directly provided by SAXS data. Nevertheless, the

scattering patterns measured at different concentrations

can be well scaled to each other, pointing out the absence

of a significant aggregation phenomenon, as confirmed by

the SDS-PAGE analysis. Further details on the experiment

can be found in [17]. The result of this experiment is

shown by the black line in Figure 3(a).

4. Selection of equilibrium configurations

We use a fit of the SAXS curve based on the ensemble

optimisation method EOM [20,21] to extract from our

simulation the set of configurations that gives the best fit of

the experimental data, as shown in Figure 3. The fitting

procedure is as follows: (i) we extract 10,000 configur-

ations of tau, regularly spaced by a 1-ps interval, from our

10 ns simulation; (ii) the theoretical scattering intensities

corresponding to these configurations are calculated by

means of the program CRYSOL [22]; (iii) these intensities

are then used by the genetic algorithm Genetic Algorithm

Judging Optimisation of Ensembles (GAJOE) [20] to

select from the initial pool an ensemble of configurations

and corresponding frequencies that provide with the

1 2 4s (nm–1)

–8–6–4–2024

ln I

(s)

Rg (nm)

0

0.04

0.08

0

0.05

0.1

0.15

Freq

uenc

y

2 4 6 8 10 12

2 4 6 8 10 12

3

(a)

(b)

(c)

Figure 3. (a) Experimental SAXS curve (black continuousline); fit by an ensemble of configurations selected by the geneticalgorithm GAJOE (red dashed line). (b) Distribution of Rg

values. Configurations produced by the simulation (blackcontinuous line) and configurations selected by the geneticalgorithm (red line), after addition of the coordinated water layer.(c) As in (b), but produced by a 30 ns standard MDsimulation.[13]

1086 A. Battisti et al.

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average their theoretical scattering curves the best fit of the

experimental SAXS data5; (iv) the theoretical SAXS

pattern of each configuration also takes properly into

account the scattering from the hydration shell of the water

layer coordinated with the molecule.[22] In this case, the

final selected ensemble entails 194 configurations, with

different statistical weights.

As shown in Figure 3(a), the selected ensemble

corresponding to these curves fits quite well the

experimental SAXS results, when each configuration is

weighted with the appropriate statistical weight as

determined by the genetic algorithm; the accuracy of the

fit is attested by the final value x2 ¼ 1:0. The distribution

of Rg values of both the original pool (black line) and the

selected ensemble (red line) is shown in Figure 3(b); the

range of Rg values of the original pool is shifted to the right

with respect to the Rg values visible in Figure 1 because

the former takes into account the hydration shell, which

adds about 0.2 nm to the Rg values.[23] The Rg values of

the ensemble selected by the genetic algorithm show a

distribution peaked near the experimental value

Rg ¼ 6:6 nm, with a significant presence of conformers

with Rg values between 3.0 and 10.5 nm. The radius of

gyration averaged over this ensemble is Rg ¼ 6:8 nm, with

a standard deviation of 1.7 nm. It is in very good

agreement with the theoretical value expected for a 441-

amino-acid random coil in solution, which is 6.9 nm.[24]

5. Tertiary structures

The thorough shaking of the molecular structure produced

by the metadynamics algorithm is clearly shown in Figures

1 and 2. This dynamics drives the system to distant points

of the phase space and thus to very different global folds.

Figure 4 displays the instant contact maps (Ca–Ca

distance between all pairs of residues) of four configur-

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100 200 300 400 100 200 300 400

100 200 300

Residue index400

0 1.5Distance (nm)

(a) (b)

(c) (d)

Figure 4. Instant contact maps (Ca–Ca distance between pairs of residues) at t ¼ 41 ps (a), t ¼ 1027 ps (b), t ¼ 4228 ps (c) andt ¼ 7567 ps (d).

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ations, chosen among the pool of 194 configurations

selected by the genetic algorithm. Three are among those

selected with highest frequency (Figure 4(a), (c) and (d));

the fourth (Figure 4(b)) further illustrates the variety of

global folds. Only distances smaller than 1.5 nm are

displayed.

The maps show a variety of global folds, with a rich

pattern of short- and long-range contacts, often forming

neat parallel or anti-parallel structures encompassing

distant segments of the primary sequence. At t ¼ 41 ps, the

proline-rich domain and the C-terminal are crumpled,

whereas the N-terminal is locally folded; the limited long-

range contact between the N-terminal (around residue 30)

and the C-terminal (around residue 430) has been

experimentally detected in a hairpin global folding.[9]

At t ¼ 1027 ps, those features have intensified and

extended, except the long-range contact between the N-

and C-terminal, which has disappeared; instead, there is an

extended proximity of the N-terminal to the repeats

domain, with a clear hairpin-like anti-parallel contiguity of

residues 100–150 to 240–300 of the first (R1) and second

(R2) repeat, and a less ordered contiguity of residues 1–

100 with residues 280–340 of the R2 and R3 repeats, the

latter repeat undergoing a local folding.

At t ¼ 4228 ps, the N-terminal, the proline-rich

domain and the C-terminal of the molecule are less

crumpled; the anti-parallel contiguity between the N-

terminal and repeats domain has extended to part of the

proline-rich domain, encompassing residues 90–170 on

one side and residues 220–310 on the other; moreover,

there is a new pattern of long-range parallel contacts

between the same stretch of the N-terminal and the C-

terminal, which in its turn is folded near the same 220–310

residues of the repeats domain, forming a paperclip-like

tertiary structure entailing residues R1 and R2; residues R3

and R4 are partially crumpled. Figure 5 shows a partial

snapshot of the molecule at t ¼ 4228 ps; only segments

relevant to the described tertiary structure are displayed.

At t ¼ 7567 ps, the molecule displays an evolved

structure entailing both a paperclip and a hairpin. The N-

terminal is in proximity of both the central segment of the

molecule and the C-terminal: residues 60–90 are near

repeats R2 and R3 (anti-parallel) and R4 (parallel);

residues 90–110 are near repeat R1 (anti-parallel); and

residues 120–200 form with residues 200–270, an anti-

parallel hairpin pattern centred in the proline-rich domain;

the residues 100–150 of the N-terminal are in long-range

contact with the C-terminal, which is folded at its centre in

a local hairpin; moreover, the region entailing repeats R1,

R2 and R3 forms an anti-parallel hairpin pattern with

repeat R4 and part of the C-terminal. Figure 6 shows a

partial snapshot of the molecule at t ¼ 7567 ps; only

Figure 5. Instant snapshot at t ¼ 4228 ps. Blue: residues 90–170; red: residues 220–310; yellow: residues 400–441.

Figure 6. Instant snapshot at t ¼ 7567 ps. Blue: residues 120–200; red: residues 200–270; yellow: residues 400–441.

1088 A. Battisti et al.

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segments relevant to the described tertiary structure are

displayed.

What is a typical lifetime of such global folds? An

estimate of a lower bound can be derived from a 30-ns

standard MD simulation of tau at the same temperature,

which produced a contact map of similar complexity.[13]

Therefore, an educated guess of the lower bound of the

global folds’ lifetime of this IDP is of the order of some

tens of nanoseconds.

Because of the totally disordered character of tau, an

average over all equilibrium global folds should not yield a

preferred pattern. This is confirmed by the contact map

averaged over all configurations selected by the genetic

algorithm, each configuration being weighted with its

frequency. The result of the averaged Ca–Ca distance

between all pairs of residues is displayed in Figure 7(a)

and does not show any significant pattern. The molecule

wanders among very different and characteristic shapes,

but at equilibrium none is statistically more relevant than

the others.

This result is confirmed by a different method, using

EOM to generate a pool of static conformers spanning the

protein’s conformational space, than selecting from this

pool by means of the iterative genetic algorithm GAJOE

the ensemble of conformers that best fits the experimental

data. We thus create a pool of 10,000 representative

backbone models of the protein using the program

RANCH.[20] We apply to this pool of conformers the

same procedure used to select an equilibrium ensemble

from the configurations produced by our 10 ns metady-

namics: the theoretical scattering intensities corresponding

to the conformers are calculated by means of the program

CRYSOL; these intensities are then used by the genetic

algorithm GAJOE to select from the initial pool an

ensemble of conformers that provides, when averaged

with the frequencies attributed by the genetic algorithm,

the best fit of the experimental SAXS data. The averaged

contact map resulting from this procedure, shown in

Figure 7(b), is practically indistinguishable from the

previous one, confirming the lack of a stable tertiary

structures at equilibrium.

6. Discussion

The simulation of an IDP is subject to the choice of a

suitable force field. Molecular mechanics force fields have

been parametrised on folded protein structures and may

not correctly reproduce the structure of disordered

proteins; therefore, a caveat is necessary when they are

used to simulate disordered proteins. On the other hand,

there is no alternative to the use of one of the known force

fields because an ab initio calculation of a large molecule

is unfeasible. Previous simulations of segments of tau or

other IDPs have been done using force fields computed to

reproduce known globular proteins.[23,25,26] The

ffG53a6 force field we used in a previous molecular

dynamics simulation of tau provided a statistical measure

of local transient secondary structures that agreed with

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Distance (nm)0 1.5

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(b)

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200100 300 400

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idue

inde

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Residue index0 15Distance (nm)

(a)

Figure 7. (a) Averaged contact map of the equilibrium ensemble selected from the metadynamics configurations. (b) Averaged contactmap of an ensemble of conformers selected by the EOM method.

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experimental results; but the force field was less effective

in maintaining over long times an extended conformation

of the molecule.[13] A first advantage of the use of

metadynamics is that it overcomes this problem as its

algorithm avoids the risk of shrinking of the molecule by

forcing its structure up and down the Rg range, as shown in

Figure 1.

A second advantage of using a metadynamics

simulation is the production of a large pool of different

configurations of the molecule, spanning a large portion of

its phase space. But as the dynamics is progressively

biased against regions where the molecule has already

been, its statistical outcome has to be checked with

suitable experimental data. This has been done by fitting

the SAXS data with the pool of configurations, as detailed

in Section 4. The cyclic application of the genetic

algorithm GAJOE to select the best ensemble of

configurations progressively yields an improved fit of the

SAXS data. Figure 8(a) shows the evolution of x2 during

the implementation of the GAJOE algorithm, encompass-

ing 1000 cycles; the final value is x2 ¼ 1:0. This is

significantly better than the value 1.4 found by fitting the

same SAXS data with the configurations selected from a

30-ns standard MD simulation at T ¼ 300 K, as shown in

[13]. It is interesting that the latter fit starts with a lower

value of x2 due to the concentration of the configurations

near the centre of the distribution as shown in Figure 3(c)

but yields at the end a higher value of x2; this shows again

that the statistical sampling of tau’s phase space achieved

by metadynamics is better than the one achieved by

standard molecular dynamics.

The higher efficiency of metadynamics in sampling

different regions of the phase space, in comparison to a

standard MD simulation of similar duration, is reflected in

the distribution of the Rg values before and after the

selection performed by means of the genetic algorithm.

This can be seen by comparing (b) and (c) in Figure 3,

where the original pool in (b) encompasses a much broader

range of Rg values than in (c), that derives from the

already-mentioned 30-ns standard MD simulation and the

subsequent application of the same genetic algorithm.[13]

Also, the selected ensemble distribution shown in Figure

3(b) appears to be statistically more significant than the

one shown in Figure 3(c), the former being approximately

centred on the experimental value Rg ¼ 6:6 nm. It can also

be noted that the selected distribution in Figure 3(b) is

similar to but broader than the one derived by applying the

EOM procedure to produce a pool of static conformers of

tau.[10]

The metadynamics algorithm drives the system to

distant points of the space phase, improving the statistical

sampling by producing likely and less likely configur-

ations. Due to this drive, transient tertiary structures last

short times, probably shorter than their natural lifetime in

an unbiased dynamics. Therefore, a contact map of the

molecule averaged over all configurations produced by the

metadynamics simulation – not just those of the selected

equilibrium ensemble – could highlight only resilient

tertiary structures, if any. Figure 9 shows the contact map

of the protein computed during the 10-ns metadynamics

trajectory. This map clearly shows that the statistically

more relevant tertiary pattern displays a long segment

encompassing the N-terminal and the proline-rich domain

(residues 120–190) in anti-parallel proximity of a segment

encompassing the proline-rich domain and the repeats

200 400 600 800 10000

2

4

6

8

200 400 600 800 1000Generations

1

1.5

2

2.5

3

χ2χ2

Figure 8. Evolution of x 2 for the SAXS data fit during the cycleof the GAJOE genetic algorithm that yields the best fit. (a)Metadynamics simulation of 10 ns. (b) Standard moleculardynamics simulation of 30 ns.[13]

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400

100 200 300 400

Residue index

Distance (nm)0 1.5

Res

idue

inde

x

Figure 9. Contact map (mean smallest distance between pairsof residues) averaged over 10 ns of metadynamics at T ¼ 300 K.

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domain (residues 200–280). These two segments must

thus be joined by a turn taking place around residue 195,

right in the middle of the proline-rich domain. It is

noteworthy that the end of the hairpin (residues 275–280)

is the hexamer VQIINK, known to be involved in the

aggregation process leading to the formation of

PHFs.[25,27,28]

The tertiary pattern described in the previous

paragraph is embedded in various hairpin or paperclip

transient tertiary structures, as shown by comparing Figure

9 with Figure 4(b)–(d). The contact map in Figure 9

differs from that in Figure 7 because the former takes into

account all configurations produced by the metadynamics,

including those statistically less relevant, whereas the

latter is strictly based on the selected set of configurations

representing the most frequent structures at equilibrium.

In conclusion, our simulation shows that a 10-ns

trajectory of metadynamics provides a significant obser-

vation of the overall fold of the molecule, generating many

configurations widely distributed in the phase space. The set

of configurations selected from the simulated dynamics by

fitting the SAXS data is the best approximation of an

equilibrium ensemble that can be extracted from a 10-ns

dynamics, and displays relevant features of overall transient

tertiary structures of tau. In particular, this set entails both

hairpin [3,7,8] and paperclip conformations [9–11], i.e. the

conformations believed to be a precursor stage of the

polymerisation of tau leading to the formation of fibrils and

to the onset of neurodegenerative diseases. Although all

those conformations are transient, the more lasting tertiary

pattern is a hairpin folding encompassing part of the N-

terminal, the proline-rich domain, the first repeat and a

functionally relevant part of the second repeat.

Acknowledgements

The authors are indebted to Dr Petra Pernot for providing accessto the beamline at ESRF and for assistance during theexperiment. The computer simulation was supported byCASPUR (Italy) under a Standard HPC Grant 2012 (std12-039).

Notes

1. The data bank DisProt (http://www.disprot.org) lists nearly700 disordered proteins; the entry for tau is DP00126.

2. A description of the different isoforms can be found athttp://www.uniprot.org/uniprot/P10636

3. GROMACS release 4.5.3, http://www.gromacs.org; boxvolume, 15,253 nm3; ffamber99 force field; SPC/E watermodel; time step, 2 fs; modified Berendsen thermostat,Parrinello–Rahman pressure coupling.

4. CV ¼ Rg; deposition stride, t ¼ 10 ps; heightW ¼ 0:5 kJ/mol; Gaussian width, s ¼ 0:35 nm; limits onRg: upper UW ALL ¼ 7.0 nm, lower LW ALL ¼ 5.5 nm.

5. GAJOE parameters were set as follows: number ofgenerations, 1000; number of ensembles, 50; number of

curves per ensemble, 20; number of mutations per ensemble,10; number of crossings per generation, 20.

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