Shedding Light on the Dock–Lock Mechanism in Amyloid Fibril Growth Using Markov State Models

We investigate how the molecular mechanism of monomer addition to a growing amyloid fibril of the transthyretin <i>TTR</i>_105–115 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

Lipid bilayer mixing.

<p>We show the conditional entropy quantification of mixing in a lipid bilayer, obtained using definitions NB-cutoff () and NB-weight (8 states) for the state of the neighbourhood. The data were obtained from a coarse-grained molecular dynamics simulation of a biomembrane consisting of 504 POPC (red) and 1512 POPE (green) lipids with the MARTINI forcefield <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065617#pone.0065617-Marrink1" target="_blank">[25]</a>.</p

Brownian dynamics of mixing and demixing.

<p>Different snapshots of a coarse-grained Lennard-Jones (CG-LJ) binary fluid membrane of particles are shown. Mixing is followed from (A) at , (B) at and (C) at ; demixing takes place from (D) at , (E) at and (F) at .</p

Entropy of the Ising model.

<p>Entropy per particle for the Ising model on a square lattice as a function of the temperature . (A) Glauber Dynamics (200×200 lattice). (B) Kawasaki dynamics with fixed zero magnetisation (100×100 lattice). We estimated from equilibrium ensembles of Monte-Carlo simulations using different approximations: mean field, Kikuchi and conditional entropy. In (A) we also compare our results with the exact solution obtained by Onsager <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065617#pone.0065617-Onsager1" target="_blank">[2]</a>. The neighbourhood in is defined as the set of lattice sites within a maximum distance and in the upper half-plane from each site.</p