Structural Insight into Tau Protein’s Paradox of Intrinsically Disordered Behavior, Self-Acetylation Activity, and Aggregation

Tau is an intrinsically disordered protein (IDP) implicated in Alzheimer’s disease. Recently, tau proteins were discovered to be able to catalyze self-acetylation, which may promote its pathological aggregation. Understanding the paradox of tau’s random-like conformations, aggregation propensity, and enzymatic activity are challenging questions. We characterized the atomic structures of two truncated tau constructs, K18 and K19, consisting of, respectively, only the four- and three-repeats of tau protein, providing structural insights into tau’s paradox. Extensive 4.8 μs replica-exchange molecular dynamics simulations of the tau proteins achieved quantitative correlation with experimental Cα chemical shifts. Our results revealed (1) dynamically ordered conformations with close lysine–cysteine distances essential for tau self-acetylation and (2) high β-sheet content and large hydrophobic surface exposure for the two critical hexapeptides (275VQIINK280 and 306VQIVYK311), crucial for tau aggregation. Together, they illuminate tau’s perplexing behavior of how its disordered state can accomplish both roles.


Initial state of K18 and K19 monomers
For each REMD simulation, 24 different starting states were used: five of them were generated using I-TASSER 1-3 --an online server based the iterative threading assembly refinement algorithm; ten of them were generated using the online server QUARK 4 --a template-free protein structure prediction program using continuous structure fragments and optimized knowledge-based fore field; five of them are generated using Robetta 5 --an online server based on comparative modeling or de novo Rosetta fragment insertion method; one of them was generated using the SAM-T06 6-7 --an online protein structure prediction server based on hidden Markov models (HMM-based); while the other three are modeled with U-turn structures 8 . Previous MDsimulation and double electron−electron resonance spectroscopy studies suggested that the amyloid filaments of K18 and K19 are ensemble of U-turn motifs [8][9] . To examine whether such S2 U-turn motifs are populated in the monomeric forms of K18 and K19, we selected three conformations with U-turn motifs as the starting states of REMD simulations. Figures S1 shows the 24 initial states of REMD runs for (A) K18 and (B) K19.

REMD simulations
We explored the conformational space of tau K18 and K19 monomers using replica exchange molecule dynamics (REMD) simulations [10][11][12] with explicit water. Explicit-solvent REMD simulation has been shown to be able to reveal the conformational organization of small disordered histone tails 13 . Two REMD simulations were performed using the GROMACS-4.5.3 software package 14 with all-atom CHARMM27 force field 15 . The simulations were conducted in the NPT ensemble using 48 replicas. The exchange time between two adjacent replicas is 1 ps and the average acceptance ratio is 16%. In the REMD simulations, the temperatures were maintained at the chosen values using the velocity rescaling method 16 with a coupling constant of 0.1 ps. The pressure was kept at 1.0 atm with a coupling constant of 1 ps via the Parrinello-Rahman barostat 17 . Bond lengths within peptides and water molecules were respectively constrained by the LINCS 18 and the SETTLE 19 algorithms. This allowed an integration time step of 2 fs. A twin-range cutoff of 0.9/1.4 nm was applied for van der Waals interactions and the particle mesh Ewald method was used to calculate the electrostatic interactions with a real space cutoff of 0.9 nm. All simulations were performed using periodic boundary conditions. The protein molecules were explicitly solvated in a TIP3P water box with a minimum distance of 1.0-1.8 nm from any edge of the box to any protein atom. The Na+ and Cl-were added to the solution with an ion concentration of 0.1 M.
For each REMD simulation, the 24 different starting conformations were evenly distributed in 48 different temperatures (replicas) ranging from 310-430 K. Each replica was run for 100 ns (a total simulation time is 4.8 s), and the last 70 ns of trajectories at T=310 K were used for analysis, which represent 70,000 conformations (one conformation was taken every 1 ps). In the rmsd-based cluster analysis, only 14,000 conformations (one conformation was taken every 5 ps) were used as the computer memory will be exceeded if the matrix is larger than 14,00014,000.
In this study, except for the rmsd-based cluster analysis, we used 70,000 conformations for all other analyses. We checked the final structures at t=100 ns, and basically excluded the possibility that the final structures are biased by the initial conformations (see Fig. S1).

Analysis
All results reported in this study refer to the REMD sampling collected at 310 K. The intramolecular interactions were analyzed by the probability of residue-residue contact maps.
Here, a contact is defined when carbon atoms of two non-sequential residues come within 0.54 nm or any other non-hydrogen atoms of two non-sequential residues lie within 0.46 nm 20 . A salt bridge between a pair of oppositely charged residues is considered to be formed if the centroids of the side-chain charged groups in oppositely charged residues lie within 0.4 nm of each other 21 .
The DSSP program was used to determine the secondary structure 22 . The SPARTA program is used to predict the C  chemical shift 23 . The free energy landscape was constructed using the relation -RT lnH(x,y), where H(x,y) was the histogram of two selected reaction coordinates, x and y. In the analysis of spatial distribution of helical and -sheet structures, the x coordinate is the distance of the helical structure from the protein's centroid and the y coordinate is the distance of the -sheet structure from the protein's centroid. In the analysis of hydrophobic and hydrophilic solvent accessible surface area (SASA) distribution, the x coordinate is the hydrophobic SASAs, and the y coordinate is the hydrophilic SASAs. RMSD-based cluster analysis was performed to investigate the atomic structures of K18 and K19. With a C  -RMSD cutoff of 0.4 nm, the K18 and K19 monomers were separated into 289 and 262 clusters, respectively.

Convergence of REMD simulations
The convergence of the two REMD simulations for K18 and K19 was verified by monitoring the conformational evolution in temperature space, by comparing: the probability of secondary structure contents, the probability density function (PDF) of radius gyration (Rg) and solvent accessible surface area (SASA) of K18 and K19, and the alpha-helix, -strand, turn and coil percentages of both K18 and K19 as a function of amino acid residues within two different time intervals (30-65 and 65-100 ns), and by comparing our calculated secondary chemical shifts of C  atoms with those from previous NMR experiments 24 . As seen from Fig. S2, the highly structured conformers of K18 and K19 can evolve from random or partially structured conformations. Figures S3 and S4 shows that the probability of secondary structure contents, the PDF of Rg and SASA of K18 and K19, and the secondary structure percentages of each residue within the two different time intervals are quite similar. We have calculated the number of clusters within the two time windows for both K18 and K19 using a C  -RMSD cutoff of 0.4 nm.

S4
The numbers of clusters are listed in Table S1 and they are close to each other. We have also calculated the C  -RMSD of each of the first eight clusters in Figure 2 with each of the 24 initial structures after equilibration. Table S2 lists the smallest C  -RMSD value of the first eight clusters with one of the 24 initial states. It can be seen form Table S2  Taken together, our data indicate converged sampling of conformational space of the large K18 and K19 proteins.

-helical and -sheet structures in K18 and K19 monomers
Conversion of -helix into -sheet is frequently observed in the process of amyloid formation, as in the case of native insulin 27 , designed peptides 28 , amyloid β-protein (A) 29 and more. We found the populations of helical structures are higher than -structures in each repeat. In K18, the probabilities to form helix and -sheet structures are respectively 11.15% and 7.35% for R1, 16.76% and 12.59% for R2, 14.28% and 10.35% for R3, and 22.41% and 4.52% for R4. In K19, the probabilities for R1 to form helical structure and -structure are 25.41% and 8.31%, respectively, 18.70% (helical) and 14.40% () for R3, where 22.37% (helical) and 11.54% () for R4.
In K18, the non-local -sheets can be divided into five major types (Figure 2 (B1a-B1b in C8); (iv) anti-parallel -sheet formed by the N-terminal of R3 and R4 (B1b-B1c in C3). Overall, K19 forms larger -sheets than K18, for example, -sheet with four strands B1a-B1b-B1c-B1d is seen in clusters 3 and 7, while in K18, the largest -sheet is three-stranded sheet in clusters 3, 5, and 8. In addition, -strands in K19 are usually longer than those in K18.

Contact probability maps and the spatial distribution of the secondary structures
By examining the global residue-residue and side-chain--side-chain (SC-SC) contact probability, we found that there are distinct differences between K18 and K19 conformations ( Fig. S7(A) and (B)). In K18, repeat R1 has strong interaction with R2, and R3 has strong interaction with R4, consistent with previous studies 30

K18 and K19 monomers have different salt-bridge distributions
Structural details of K18 and K19 fibrils have been revealed through combined experimental and computational approaches [8][9]31 , indicating the existence of similar but polymorphic core S6 structures for both K18 and K19 tau filaments. Solid state NMR also found polymorphic core structures in the K19 fibril 32 . These studies indicated that the third repeat in K19 forms the rigid core, and Cys322-Gly323 could form kinks that disrupt the -strands [8][9]32 . The seeding barrier between K18 tau and K19 tau indicated that there are differences in fibril structures 33 and in monomeric properties.
Interactions between different repeats in K18 and K19 were mainly stabilized by electrostatic interactions. They are likely to promote fibril growth via peptide addition along the fibril axis [8][9]31 . Since tau is a highly charged protein, with 21 positively charged residues and 11 negatively charged residues in K18, and with 16 positively charged residues and 9 negatively charged residues in K19, it is interesting to investigate the salt-bridge distributions in the monomers. We calculated all the salt bridges formed in K18 and K19 at T=310 K, using the data from 30 ns to 100 ns with a total of 70,000 conformations. Figure S10 shows the histogram of the number of salt bridges with respect to the number of intervening residues (NI). Here, the number of intervening residues is the number of residues separating the two salt-bridging residues in the sequence. Most of the salt bridges are formed between sequentially close residues in both K18 and K19 (NI≤11). In K18 ( Figure S10 (A)), there are three dominant long-range salt bridge distributions with the peak around NI=27, 41, and 66. However, in K19 (Fig. S10 (B)), there are several long-range salt bridge distributions with the peak located at NI=27, 36, 43, 50, 54, 58 and 73.
We also calculated the average number of intra-repeat and inter-repeat salt bridges (Table S3)     replicas initially set at high temperature, indicating sufficient sampling of the replicas in temperature space. We selectively analyze the top five replicas with the highest persisting populations at 310 K. For K18, the conformations in replicas 0, 24, 26, and 28 are initially random coiled and that in replica 30 is partially structured. However, at the end of the simulation, all of these replicas have evolved into partially structured conformations, and the conformation in replica 30 is highly structured (Fig. S2(C)). For K19, two of the top five replicas are initially random and three are partially structured (Fig. S2(D)). Similar to K18, the initial conformations of K19 also experience random coil to -helix/-sheet (or vice versa) transitions (for example, Repl. ID 28 and Repl ID 2 in Fig. S2(D)). These results indicate K18 and K19 are not trapped in local energy minimum.     often cooperatively trigger fibril formation in long amyloidogenic sequences [ 35 ]. As seen from Figure S9, the most populated -strand lengths in both K18 and K19 range from 2 to 5. The large variation of SASA from 0~400 Å2 indicates that these stretches can be buried or exposed to solvent. In the fibril structural models of K18 and K19 with a fully extended repeat [8][9]31 , the long -strand stretch can span 20 residues. It is interesting to see what re-arrangements are needed to change the short -sheet stretches to fully extended repeats. In our simulations, we found that there are some residual -structures located in the C-terminal of R1, R2, R3 and R4, and the Nterminal of R2, R3, and R4, most of which form local -hairpin structures between the Cterminal of one repeat and the N-terminal of the next. However, in the first eight clusters, we found some non-local -sheet structures linking more than two repeats. In K18, the -sheets B1a-B1b-B1c in C3 (5.67%) and C8 (2.64%) linking R1-R2-R3 together and the -sheet B1a-B1b-B1c in C7 (2.79%) linking R2-R3-R4, located outside of the compact structure, are partially exposed to the solvent and keep the elongated faces towards to the solvent (Fig. 2(A)). In K19, the -sheet B1a-B1b-B1c-B1d in C3 (6.94%) and C7 (2.37%) linking R1-R3-R4 also exist ( Fig.   2(C)). Therefore, the topologies of the short -stretches indicate that they may need to be reorganized upon -stretch elongation. Figure S10. Histograms show the count of salt bridges with respect to the number of intervening residues for K18 and K19 at 310 K. The number of intervening residues is the number of residues separating the two salt-bridging residues in the sequence.