Kinetics of spontaneous filament nucleation via oligomers: Insights from theory and simulation

Abstract

Nucleation processes are at the heart of a large number of phenomena, from cloud formation to protein crystallization. A recently emerging area where nucleation is highly relevant is the initiation of filamentous protein self-assembly, a process that has broad implications in many research areas ranging from medicine to nanotechnology. As such, spontaneous nucleation of protein fibrils has received much attention in recent years with many theoretical and experimental studies focussing on the underlying physical principles. In this paper we make a step forward in this direction and explore the early time behaviour of filamentous protein growth in the context of nucleation theory. We first provide an overview of the thermodynamics and kinetics of spontaneous nucleation of protein filaments in the presence of one relevant degree of freedom, namely the cluster size.In this case, we review how key kinetic observables, such as the reaction order of spontaneous nucleation, are directly related to the physical size of the critical nucleus. We then focus on the increasingly prominent case of filament nucleation that includes a conformational conversion of the nucleating building-block as an additional slow step in the nucleation process. Using computer simulations, we study the concentration dependence of the nucleation rate. We find that, under these circumstances, the reaction order of spontaneous nucleation with respect to the free monomer does no longer relate to the overall physical size of the nucleating aggregate but rather to the portion of the aggregate that actively participates in the conformational conversion. Our results thus provide a novel interpretation of the common kinetic descriptors of protein filament formation, including the reaction order of the nucleation step or the scaling exponent of lag times, and put into perspective current theoretical descriptions of protein aggregation.2

Dynamics of oligomer populations formed during the aggregation of Alzheimer’s Aβ42 peptide

“…The free energy barrier for oligomer conversion is lower at higher monomer concentrations, which explains the observation that the fraction of oligomers that dissociate without forming new fibrils is lower at higher monomer concentrations. The non-classical nucleation behaviour described here for Aβ42 fibril formation is analogous to the two-step nucleation processes observed in crystallisation, bio-mineralisation and sickle-cell haemoglobin 26,27,[34][35][36][37][38][39]. Moreover, we have established the absence, in our system, of detectable quantities of persistent off-pathway oligomers that cannot convert to fibrils over the timescale of aggregation, although such species may exist under different experimental conditions or for other, particularly larger, amyloidogenic proteins such as α-synuclein 40.…”

“…The non-classical nucleation behaviour described here for Aβ42 fibril formation is analogous to the two-step nucleation processes observed in crystallisation, bio-mineralisation and sickle-cell haemoglobin. 26,27,[34][35][36][37][38][39] Moreover, we have established the absence, in our system, of detectable quantities of persistent off-pathway oligomers that cannot convert to fibrils over the timescale of aggregation, although such species may exist under different experimental conditions or for other, particularly larger, amyloidogenic proteins such as α-synuclein. 40 More generally, our work could be extended to study oligomer dynamics in peptide mixtures; in the presence of additional inhibitors, 41 11 these experiments could inform upon the role of off-pathway oligomers in such systems.…”

Scaling behaviour and rate-determining steps in filamentous self-assembly

“…If required, it can be extended to account for a less coarse-grained description of the individual processes, such as for example a multi-step process with on-pathway oligomers for primary nucleation. 16–18 By analogy with the mathematical description, the abstraction to the fibril number and mass concentrations allows the reduction of a very large, complex reaction network that considers every species individually, to a much simpler, compact one as shown in Fig. 2.…”

“…7. The approach presented here to link the scaling exponent to the network topology is general and can be easily extended to variations and extensions of the Petri net, for example to account explicitly for the presence of oligomeric species 18 or to take into account the formation of higher order assemblies from existing aggregates. 31 …”

Physical mechanisms of amyloid nucleation on fluid membranes

“…The minimal model for the amyloid-forming proteins is based on the coarse-grained model introduced in Refs. [20,21]. Proteins are modelled as hard patchy spherocylinders and can exist in two distinct conformational states: a soluble (s) and a β-sheet forming (β) confor-mation, both of which are equipped with different arrangements of interaction patches.…”