Letter pubs.acs.org/JPCL
Shedding Light on the Dock−Lock Mechanism in Amyloid Fibril Growth Using Markov State Models Marieke Schor,*,† Antonia S. J. S. Mey,‡ Frank Noé,‡ and Cait E. MacPhee† †
School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom Department for Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, Berlin 14195, Germany
‡
S Supporting Information *
ABSTRACT: We investigate how the molecular mechanism of monomer addition to a growing amyloid fibril of the transthyretin TTR105−115 peptide is affected by pH. Using Markov state models to extract equilibrium and dynamical information from extensive all atom simulations allowed us to characterize both productive pathways in monomer addition as well as several off-pathway trapped states. We found that multiple pathways result in successful addition. All productive pathways are driven by the central hydrophobic residues in the peptide. Furthermore, we show that the slowest transitions in the system involve trapped configurations, that is, long-lived metastable states. These traps dominate the rate of fibril growth. Changing the pH essentially reweights the system, leading to clear differences in the relative importance of both productive paths and traps, yet retains the core mechanism.
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Markov state models (MSMs). MSMs have been shown to be a very useful tool in extracting equilibrium and dynamic information from complex MD simulations, in particular enabling predictions of long time-scale kinetics from relatively short simulation trajectories.9−12 A further advantage of using MSMs is that they can be used to quantify dynamic pathways such as folding pathways.13 This concept can be applied to the TTR105−115 amyloid fibril to shed light on the dock−lock mechanism at different pH values. While a low pH is essential to initiate fibril formation, previous nanoelectrospray ionization mass spectrometry and ion mobility mass spectrometry experiments have shown that oligomers larger than dimers carry fewer charges than the number of constituent peptides,14 indicating that deprotonation is essential to stabilization of larger oligomers. This was corroborated by MD simulations, where the stability of several oligomers consisting of either protonated or deprotonated peptides was compared.15 Hence, fibril growth after seed formation is likely to involve deprotonated peptides. To confirm that, once nucleated, TTR105−115 fibrils can grow at both low and neutral pH, we compared kinetic growth curves of monomeric peptide solutions (at neutral and acidic pH) seeded with fibrils preformed at pH 2, obtained by monitoring the fluorescence of the amyloid-specific dye thioflavin T (ThT) (Figure SI3 in the Supporting Information (SI)). Seeding indeed results in fibril formation under both conditions; however, growth is initially slower at neutral pH. Please refer to the SI for more information about these experiments.
any proteins and short peptides can self-assemble into long, highly ordered structures called amyloid fibrils. Such fibrils are most commonly associated with diseases like Alzheimer’s and type 2 diabetes, although more recently functional amyloid-like fibrils have been discovered.1,2 Moreover, such systems have received a lot of interest as potential bionanomaterials.3 Recent advances in solid-state NMR (ssNMR) and X-ray crystallography have provided a number of atomic resolution fibril structures. However, the process of fibril formation is not well understood and involves several steps. Nucleation, where peptides assemble into often relatively disordered oligomers followed by a transition into a small, stable seed with a more regular structure is typically regarded as the first step. The resulting seeds can grow, fragment, and function as a template for secondary nucleation.4 Subsequent fibril growth is thought to occur through sequential incorporation of peptide monomers. Monomer addition is essentially a two-step process that is referred to as the dock−lock mechanism.5,6 In the first (docking) step, the peptide forms an initial contact with the fibril template. Docking is followed by the much slower locking step, where the peptide changes conformation until it fits the fibril template perfectly.5,7 In principle, multiple docked states could lead to a correctly configured, fibril-incorporated peptide. One could imagine incorrect docking leading to off-pathway metastable states,8 which would slow down the dock−lock transition significantly. We will address the role multiple docked states play in fibril growth of the transthyretin TTR105−115 peptide using a series of molecular dynamics (MD) simulations. In particular, we will look at the role of pH on the monomer addition process. To ensure an optimal analysis of the simulation data, we will use © 2015 American Chemical Society
Received: February 13, 2015 Accepted: March 10, 2015 Published: March 10, 2015 1076
DOI: 10.1021/acs.jpclett.5b00330 J. Phys. Chem. Lett. 2015, 6, 1076−1081
Letter
The Journal of Physical Chemistry Letters
Figure 1. MSM analysis. The implied time scales, ti, of the three slowest processes at low (A) and neutral (B) pH are shown. Kinetic maps of the MSMs at low (C) and neutral (D) pH allow the identification of which microstates interconvert on the slowest two time scales shown in panels A and B. The eigenvectors ϕ2−ϕ3, with their 150 discrete microstates corresponding to λ2 and λ3, respectively, are plotted against each other and colorcoded according to the metastable clusters identified using PCCA. (See Figure 2 and SI Figure SI5.) The molecular structures associated with the slowest transitions are shown in panels E and F.
ns with a Chapman−Kolmogorov test. (See the SI.) Therefore, for both MSMs, at low and neutral pH, 20 ns was chosen as the lag time for all further analysis. States that are kinetically most disconnected can be identified from a so-called kinetic map, which is obtained by plotting the second and third eigenvectors against each other (as explained in SI Figure SI1). Transitions between these states are responsible for the slowest time scales observed in the systems. Kinetic maps for the system at low and neutral pH are shown in Figure 1C,D, respectively. At low pH, the slowest transitions are between structures, where the locking peptide (P6; see SI Figure SI2) interacts primarily through its hydrophobic side chains (Ile, Ala, and Leu) with the terminal peptide of the sheet below (P3) (green box in Figure 1E) and structures where P6 chain is relatively extended and interacting with the terminal peptides of both sheets in the fibril (yellow box in Figure 1C). The second slowest transition also involves this same extended structure and the fibril state (red box in Figure 1E). The time scales associated with these two transitions are t2 ≈ 10 μs and t3 ≈ 2 μs, respectively. (See Figure 1A.)
Subsequently, we ran extensive all-atom MD simulations to explore the internal rearrangements involved in the ratelimiting monomer locking step in fibril growth at low and neutral pH. By looking at a free-energy projection for both pH values on to the first two time-lagged independent component analysis (TICA) coordinates based on the 40 selected distances (SI Table 1), it can be seen that both data sets sample largely overlapping regions (SI Figure SI4). However, there are clear differences in location of minima and barriers, indicating that different conformations are favored at each of the pH values. We now construct MSMs from our set of short (50 × 100 ns per pH) trajectories to assess the long-time scale behavior of the systems.11,16 To ensure that the MSM for each pH obeys the Markov property, we evaluated transition matrices P(τ) at different lag times, τ. The implied time scales were then calculated according to eq 4 in the SI. In Figure 1A,B we show the convergence of the implied time scales t2, t3, and t4 for low and neutral pH, respectively. In both cases for the slowest decaying eigenvalue we observe mostly converged time scales at lag times of τ > 20 ns. We further validated the choice of τ = 20 1077
DOI: 10.1021/acs.jpclett.5b00330 J. Phys. Chem. Lett. 2015, 6, 1076−1081
Letter
The Journal of Physical Chemistry Letters The structures involved in the slowest two transitions at neutral pH are clearly different from those identified at low pH. The slowest transition involves conversion between structures, where P6 sits between the upper and lower sheet and is almost fully elongated (blue box in Figure 1D) and structures where P6 is relatively compact and mostly associated with P3 (green box in Figure 1D). The second slowest process is the transition between this same compact structure and structures where P6 is elongated and associated with P3. Here P6 forms a registershifted antiparallel β-sheet with the lower sheet, which seems mostly stabilized through hydrophobic side-chain interactions. To assess the transitions involved in locking a docked monomer onto the fibril template, we construct the transition network from the transition matrix evaluated at a lag time of τ = 20 ns. For clarity, we coarse-grain the MSM by grouping our 150 microstates into 12 kinetic clusters. Kinetic clusters, or metastable states, are characterized by comparatively fast interconversions between microstates belonging to the same cluster. Transitions to other clusters are markedly slower. Using Perron cluster cluster analysis (PCCA),12 these kinetic clusters can be extracted from the transition matrix. Plotting the spatial arrangement of the 150 microstates in the TICA1−TICA2 coordinate space and coloring the microstate by kinetic cluster (Figure SI5 in the SI) shows clear differences between low and neutral pH in how the microstates are grouped into kinetic clusters, reflecting the different free-energy barriers experienced by each system. On the basis of the transition path theory (TPT)17,18 analysis of the kinetic clusters identified by PCCA, we assign a transition network onto the coarse-grained MSM (Figure 2). The mean first passage time, τmfp, for the transition from the minimally docked (light green) to the final fibril state (red) is a good estimate for the rate of monomer incorporation and can be extracted from the transition matrices of the MSMs. At neutral pH, the observed τmfp = 56 μs. At low pH, monomer incorporation is approximately a factor of two faster, with τmfp = 22 μs. To assess the contribution of the main trapped states, as identified in Figure 1C,D to the observed mean first passage times, we recalculate τmfp while excluding the traps from the network. At neutral pH, excluding the main trapped states (dark green and blue) has only a minor effect on τmfp, which decreases to 48 μs. However, at low pH, excluding the two main trapped states (dark green and yellow) reduces τmfp to 10 μs. This shows that the off-pathway trapped states contribute significantly to the rate of monomer addition at low pH. So far, we have assumed that the internal rearrangements (locking) rather than encounter times (docking) are the ratelimiting steps in monomer addition. The encounter or docking rate can be estimated using the Smoluchowski equation kon = 4 πRD, where R is the distance at which the complex is formed and D is the diffusion constant. On the basis of three dissociation trajectories, we choose R = 1.4 nm. The diffusion constant is estimated using the Stokes−Einstein relation, D = kT/(6πηRg), with the viscosity η = 0.80 mPa and the radius of gyration Rg = 0.86 nm. Combining these relations, we obtain kon = 3 × 109 M−1 s−1 for low pH. Thus, at concentrations above 1.5 × 10−5 M, the assumption that the rate of monomer addition is dominated by slow internal rearrangements holds for low pH. At neutral pH, where τmfp is larger and a more compact leads to a higher kon, the assumption holds for even lower concentrations. We will now proceed to discuss the internal rearrangements in detail.
Figure 2. Transition network for the MSM constructed at lag time 20 ns for low (A) and neutral (B) pH. Colors of the dots indicate the different kinetic clusters identified with PCCA, with the fibril state in red for both conditions. The size represents the relative population. The solid arrows indicate the productive flux in the network, with thickness corresponding to their relative contribution. Dotted lines indicate connections that do not contribute significantly to the productive flux.
The transition network at neutral pH (Figure 2B) indicates that virtually all transitions into the fibril kinetic cluster (red) occur from the cyan kinetic cluster. The vast majority of the flux into the cyan kinetic cluster comes from the highly populated brown cluster, which seems to act as a hub in the network. Starting in the minimally docked, or encounter, kinetic cluster (light green) there are several routes to this brown cluster. Notably the orange cluster, which was identified as one of the main contributors to the slow processes in the network (see Figure 1D,F), is an important intermediate here. The transition network also includes several kinetic clusters that do not contribute to the productive flux in the system (indicated with dotted arrows). Some of these states, most notably blue and dark green, represent traps. Escapes from these so-called traps correspond to the slowest processes in the locking process. (See Figure 1D,F.) A noticeable difference between the transition networks at low and neutral pH is that at low pH the trapped states furthest away from the fibril state are much more populated than at neutral pH. These trapped states consist of structures where the locking peptide is rotated away from its alignment with the top sheet and has very stable interactions with the lower sheet or both sheets (e.g., the dark green structure in Figure 1E). Another clear difference is the absence of the trapped state at (TICA1 = −2, TICA2 = 2). This state, where the locking peptide is mostly properly aligned with the top sheet but is sitting in between the two sheets, is likely to be destabilized at low pH due to lack of stabilizing interactions between the termini of the locking peptide chain and the termini of the last peptide chain of the sheet below. (See SI Figure SI2.) 1078
DOI: 10.1021/acs.jpclett.5b00330 J. Phys. Chem. Lett. 2015, 6, 1076−1081
Letter
The Journal of Physical Chemistry Letters
Figure 3. Representative structures of kinetic clusters visited on the most productive paths connecting the minimally docked to the fully locked fibril state for low (A) and neutral (B) pH. Colored borders around the structures indicate the kinetic cluster and correspond to those in Figure 2. The solid black numbers indicate the percentage of the total population found in this PCCA cluster. The cursive gray numbers next to the arrows indicate the flux. Only fluxes above 10% of the total productive flux are shown. The molecular structures are displayed as balls for every Cα atom of peptide chains P3, P5, and P6 (see SI) and colored for residue name with Y, green; T, pink; I, violet; A, blue; L, cyan; S, yellow; and P, brown. The Cα atoms of each peptide are connected by red (P5 and P6) or blue (P3) sticks to indicate the backbone trace. Key Cα contacts (Cα distance
