Stefan Auer: Highlights

Nano-particle catalyzed peptide aggregation

Illustration of the ``condensation-ordering'' mechanism of peptide self-assembly in the presence of a hydrophobic nanoparticle. (A) Initially, at t=3.9 microseconds, the peptides are in their monomeric state. (B) At intermediate times, t=0.195 milliseconds, small oligomeric assemblies form on the nanoparticle surface. (C) At later times, t=0.78 milliseconds, these oligomers re-order into fibrillar structures as their size increases. Peptides that do not form intermolecular hydrogen bonds are shown in blue, while peptides that form intermolecular hydrogen bonds are assigned a random colour, which is the same for peptides that belong to the same β-sheet. The spherical nanoparticle is displayed in orange in the centre of the simulation box [S. Auer, A. Trovato, M. Vendruscolo, PLoS Comput Biol, 5 e1000458 (2009)]. See animation 1 of the Molecular Dynamics trajectory and animation 2 a rotation of the final structure obtained.

Self-templated nucleation in peptide and protein aggregation

The nucleation mechanism by which peptides and proteins aggregate is much studied because of its implications for human health and nanoscience. Understanding the molecular basis of nucleation phenomena poses enormous challenges even for the simplest types of atoms and molecules. In the case of proteins, the situation is even more problematic since the high internal flexibility of these molecules creates a tremendous complexity in the assembly mechanism. Such a complexity has prevented so far a clear characterisation of the mechanism of protein aggregation. In this work present a general framework that enables us to characterise in detail a nucleation process leading to the formation of ordered protein assemblies. These results are obtained through extensive numerical experiments that reveal the generic nature of the nucleation barriers assoiated with peptide and protein aggregation, and explain a key feature observed in protein aggregation - the coupling between the initial formation of oligomeric assemblies and their subsequent rearrangement into a highly ordered cross-β structures.

(a) Contour plot of the nucleation barrier F(n,m) as a function of the number of peptides n that form the aggregate, and the number of inter-chain hydrogen bonds m formed inside. The black circles indicate the minima on the free energy surface, and the black line indicates a possible path that connects them. The labels (n_α,n_β) of the minima describe the structure of the oligomer, where n_α and n_βare, respectively, the number of peptides in a α-helical and β-strand structure, and n=n_α+ n_β. In the inset we illustrate the correlation for successive minima between the number of peptides in an α-helical and β-sheet conformation. (b) Snapshots of the oligomers associated with the minima. (c) Nucleation barrier for β-sheet formation, F_1(m), as a function of the number of interchain hydrogen bonds m that are formed within the oligomer. (d) Nucleation barrier F_2(n,m_max) for the formation of an oligomer of size n that can at most form m_max interchain hydrogen bonds: m_max=10 (n_β<3) (black line), m_max=20 (n_β<4) (red line), all m values included (green line) [S. Auer, C.M. Dobson, M. Vendruscolo, A. Maritan, Phys. Rev. Lett, 101, 258101 (2008)].

A condensation-ordering transition in peptide and protein aggregation

This is my first attempt to extend my work on colloidal crystallization to investigate transitions in biological systems. Here I use a novel protein model that only incorporates ingredients that are common to all proteins, such as steric constraints, hydrogen bonding and hydrophobicity, but necessary for the existence of a marginally compact phase for polymers, to investigate peptide self-assembly into highly ordered fibrillar structures known as amyloid. In this work we try to establish the existence of a generic condensation-ordering transition for peptide aggregation in which the hydrophobic interactions initially trigger the formation of disordered oligomeric aggregates (a,right panel) which subsequently reorders into a protofilament structure (b, from left to right). Peptides that do not form intermolecular hydrogen bonds are shown in blue, while peptides that form intermolecular hydrogen bonds are assigned a random colour, which is the same for peptides that belong to the same β-sheet. [S. Auer, C.M. Dobson, M. Vendruscolo, HFSP Journal, 1, 137 (2007)]. See animation 1 of the simulation trajectory and animation 2 a rotation of the final structure obtained.

Onset of heterogeneous crystal nucleation in hard-sphere colloids

Here we performed Monte Carlo simulations to study how smooth spherical seeds of various sizes affect crystallization in a suspension of hard colloidal particles. We compute the free-energy barrier associated with crystal nucleation. We find that to be effective crystallization promoters, the seed particles need to exceed a well-defined minimum size. Just above this size, seed particles act as crystallization 'catalysts' as newly formed crystallites detach from the seed [A. Cacciuto, S. Auer, D. Frenkel, Nature 428,404(2004)].

Line tension controls wall induced crystal nucleation in hard-sphere colloids

Here I performed the first quantitative calculation of a nucleation barrier in a heterogeneous system. We studied the important case of the effect of a smooth hard wall to the nucleation kinetics of hard-sphere colloids. We found that the wall dramatically reduces the nucleation barrier but does not eliminate it. The nucleation barrier is exclusively due to the line tension of the crystallite at the surface. Line tension is never considered in the classical theory of heterogeneous nucleation. The figure shows a configuration of critical nucleus that forms on the flat wall [S.Auer,D.Frenkel,Phys.Rev.Lett.,91,015703(2003)].

Polydispersity suppresses crystal nucleation in hard-sphere colloids

Experimentally it was observed in the 80's that hard sphere colloids do not crystallize if the size polydispersity exceeds about 10% of the average radius of a particle. Based on our simulations this can be explained due to the existence of a minimum barrier height. This finding is not consistent with existing theories and might be explained by the density dependence of the surface tension [S.Auer,D.Frenkel,Nature 413,711(2001)]. The figure shows the computed free-energy barriers for crystal nucleation of polydisperse suspensions of hard colloidal spheres. The free energy &Delta G* is expressed in terms of kT, where k is Boltzmann's constant and T is the absolute temperature. |&Delta&mu| (also in terms of kT) is the absolute difference between the chemical potential of the liquid and the solid. It is a measure for the degree of supersaturation. The curves are fits that have been drawn as a guide to the eye.

Critical nucleus observed in a systems of hard-sphere colloids

The figure shows a three-layer-thick slice through the centre of the crystallite of critical size. Solid-like particles are shown in yellow, and liquid-like particles in blue. The layers shown in the figure are close-packed hexagonal crystal planes. The stacking shown in this figure happens to be f.c.c.-like (that is, ABC stacking): however, analysis of many such snapshots showed that f.c.c. and h.c.p. stackings were equally likely [S.Auer,D.Frenkel,Nature 409,1020-1023(2001)].

Prediction of absolute crystal nucleation rates in hard-sphere colloids

Here I used biased Monte Carlo simulations to calculate the nucleation barrier in hard-sphere colloids, and kinetic Monte Carlo simulations to estimate the kinetic prefactor. The computed nucleation rates are predicted from first principles and provide a rigorous test for both experiments and existing theories. We found results at odds both with existing experiments and classical nucleation theory (CNT), the theory which is mostly commonly used to predict nucleation rates. We showed explicitly that the discrepancy with experiments must be attributed to problems with the analysis of the experimental data. In addition we found that CNT underestimates the nucleation barrier by about 50%. Based on our simulations this can be explained by a density dependence of the surface tension which was not considered in previous theories. The figure shows the free energy for the formation of a crystal nucleus as a function of the number of hard-spheres in the nucleus at three different volume fractions. The solid line is a fit of the numerical data to CNT having only one fit parameter, the interfacial free energy [S.Auer,D.Frenkel,Nature 409,1020-1023(2001)].