Amyloids, fibrillar assembly of (poly)peptide chains, are associated with neurodegenerative illnesses such as Alzheimer's and Parkinson's diseases, for which there are no cures. The molecular mechanisms of the formation of toxic species are still elusive. Some peptides and proteins can form functional amyloid-like aggregates mainly in bacteria and fungi but also in humans. Little is known on the differences in selfassembly mechanisms of functional and pathogenic (poly)peptides. We review atomistic and coarse-grained simulation studies of amyloid peptides in their monomeric, oligomeric, and fibrillar states. Particular emphasis is given to the challenges one faces to characterize at atomic level of detail the conformational space of disordered (poly)peptides and their aggregation. We discuss the difficulties in comparing simulation results and experimental data, and we propose new simulation studies to shed light on the aggregation processes associated with amyloid diseases.

Brownian Dynamics is the designated technique to simulate the collective dynamics of colloidal particles suspended in a solution, e.g., the self-assembly of patchy particles. Simulating the rotational dynamics of anisotropic particles by a first-order Langevin equation, however, gives rise to a number of complications, ranging from singularities when using a set of three rotational coordinates to subtle metric and drift corrections. Here, we derive and numerically validate a quaternion-based Rotational Brownian Dynamics algorithm that handles these complications in a simple and elegant way. The extension to hydrodynamic interactions is also discussed.

Particles in simulations are traditionally endowed with fixed interactions. While this is appropriate for particles representing atoms or molecules, objects with significant internal dynamics--like sequences of amino acids or even an entire protein--are poorly modelled by invariable particles. We develop a highly coarse grained polymorph patchy particle with the ultimate aim of simulating proteins as chains of particles at the secondary structure level. Conformational changes, e.g., a transition between disordered and β-sheet states, are accommodated by internal coordinates that determine the shape and interaction characteristics of the particles. The internal coordinates, as well as the particle positions and orientations, are propagated by Brownian Dynamics in response to their local environment. As an example of the potential offered by polymorph particles, we model the amyloidogenic intrinsically disordered protein α-synuclein, involved in Parkinson's disease, as a single particle with two internal states. The simulations yield oligomers of particles in the disordered state and fibrils of particles in the "misfolded" cross-β-sheet state. The aggregation dynamics is complex, as aggregates can form by a direct nucleation-and-growth mechanism and by two-step-nucleation through conversions between the two cluster types. The aggregation dynamics is complex, with fibrils formed by direct nucleation-and-growth, by two-step-nucleation through the conversion of an oligomer and by auto-catalysis of this conversion.

Amyloid formation by the intrinsically disordered α-synuclein protein is the hallmark of Parkinson's disease. We present atomistic Molecular Dynamics simulations of the core of α-synuclein using enhanced sampling techniques to describe the conformational and binding free energy landscapes of fragments implicated in fibril stabilization. The theoretical framework is derived to combine the free energy profiles of the fragments into the reaction free energy of a protein binding to a fibril. Our study shows that individual fragments in solution have a propensity toward attaining non-β conformations, indicating that in a fibril β-strands are stabilized by interactions with other strands. We show that most dimers of hydrogen-bonded fragments are unstable in solution, while hydrogen bonding stabilizes the collective binding of five fragments to the end of a fibril. Hydrophobic effects make further contributions to the stability of fibrils. This study is the first of its kind where structural and binding preferences of the five major fragments of the hydrophobic core of α-synuclein have been investigated. This approach improves sampling of intrinsically disordered proteins, provides information on the binding mechanism between the core sequences of α-synuclein, and enables the parametrization of coarse grained models.