Simulating oligomerization at experimental concentrations and long timescales: A Markov state model approach

Abstract

Here, we present a novel computational approach for describing the formation of oligomeric assemblies at experimental concentrations and timescales. We propose an extension to the Markovian state model approach, where one includes low concentration oligomeric states analytically. This allows simulation on long timescales (seconds timescale) and at arbitrarily low concentrations (e.g., the micromolar concentrations found in experiments), while still using an all-atom model for protein and solvent. As a proof of concept, we apply this methodology to the oligomerization of an Abeta peptide fragment (Abeta(21-43)). Abeta oligomers are now widely recognized as the primary neurotoxic structures leading to Alzheimer's disease. Our computational methods predict that Abeta trimers form at micromolar concentrations in 10 ms, while tetramers form 1000 times more slowly. Moreover, the simulation results predict specific intermonomer contacts present in the oligomer ensemble as well as putative structures for small molecular weight oligomers. Based on our simulations and statistical models, we propose a novel mutation to stabilize the trimeric form of Abeta in an experimentally verifiable manner.

Figure 1

(a) Oligomer distribution at the simulated concentration (14 mM). The line represents fractions of each oligomer that were directly obtained from the ensemble of simulations, the crosses are fractions predicted by a simple 5-state SCMSM, and the circles are fractions predicted by a 30-state SCMSM. The 5-state SCMSM agrees well with the raw data at longer timescales, but we needed a more detailed model (e.g., 30-state SCMSM) to pick up complete quantitative agreement at short timescales. (b) Analytic extensions to the Markov model for low concentrations (14 μM) allow the prediction of oligomer formation from the microsecond timescale (dimer) to the 10 s timescale (tetramer).

Figure 2

The autocorrelation of the interchain contact maps shows a nonsingle exponential behavior with a rapid early phase and a slow second phase (a). The slope of the slow phase indicates the time scale for tertiary structure formation for each oligomer (b). The data suggest that the time scale for tertiary structure formation in the dimer and trimers is in the hundreds of nanoseconds. The corresponding figures for intrachain contacts are similar and not shown here.

Figure 3

Timescale of oligomer species formation vs concentration (log-log.) The simulated monomer concentration was iteratively varied using the analytic component of the ACMSM, bridging the simulations with experimental and biological concentrations. Time scales are represented as mean first passage times for the resultant transition matrices. Note that for an Aβ monomer concentration of 14 nM tetramer formation is on the order of 80 years, in contrast to the nanosecond time scales when concentration is closer to that of the simulation box.

Figure 4

Markovian model for Aβ oligomerization. Our model was built using the different aggregation states as the Markov states; in a system with four chains, there are five such states: four monomers (MMMM), two monomers and one dimer (MMD), two dimers (DD), one monomer and one trimer (MT), and finally, one tetramer (Q). In addition, to include the effects of low concentration found experimentally, we discriminate EC states (in which states are close) from separated states. The rate limiting steps in the aggregation process are shown as dotted lines. The numbers associated with the transitions are transition probabilities. The significant figures were determined from the uncertainties in the transition probabilities. Some transitions with very low probability have not been shown for the sake of clarity.

Figure 5

The top tetramer clusters do not show the formation of a single hydrophobic core comprising all four chains. Instead the cores seemed to be of the form of dimer+two monomers (a) or dimer+dimer (b) or trimer+monomer (c). This suggests that trimers might be the preferred oligomer for this system. The observed tetramers are possibly loosely associated lower order oligomers. The N-terminus is shown as brown spheres, residues M35-V36 are shown as blue spheres, G37-G38 are shown as light blue spheres, and the C-terminus is shown as slate sticks. All pictures were rendered using PYMOL (Ref. 26).

Figure 6

Contact maps for monomers, dimers, trimers, and tetramers. The high density region in the upper left corner corresponds to the hydrophobic core formed by C-terminal association. The contact maps for the other aggregation states are very similar. Note that the fraction of contacts formed is per oligomeric species rather than per chain.

Figure 7

Secondary structure profiles in each aggregation state. There is some tendency to form a helix near the N-terminus and a very slight formation of a hairpin near the C-terminus. In each case, there is little or no correlation between the secondary structure and the aggregation state.

Figure 8

Aβ trimer structural properties, as shown by (a) representative cluster center and (b) an alignment of six representative trimer structures. The N-terminal residues are shown in red, and residues M35-V40 which correspond to the darkest regions in the contact map are shown in blue and cyan. The oligomers are stabilized by a hydrophobic core formed by the C-terminal regions of the chains while the N-terminal segments are solvent exposed and unstructured.