Monte Carlo simulations of protein amyloid formation reveal origin of sigmoidal aggregation kinetics

Abstract

Severe conditions and lack of cure for many amyloid diseases make it highly desired to understand the underlying principles of formation of fibrillar aggregates (amyloid). Here, amyloid formation from peptides was studied using Monte Carlo simulations. Systems of 20, 50, 100, 200 or 500 hexapeptides were simulated. Association kinetics were modeled equal for fibrillar and other (inter- and intra-peptide) contacts and assumed to be faster the lower the effective contact order, which represents the distance in space. Attempts to form contacts were thus accepted with higher probability the lower the effective contact order, whereby formation of new contacts next to preexisting ones is favored by shorter physical separation. Kinetic discrimination was invoked by using two different life-times for formed contacts. Contacts within amyloid fibrils were assumed to have on average longer life-time than other contacts. We find that the model produces fibrillation kinetics with a distinct lag phase, and that the fibrillar contacts need to dissociate on average 5-20 times slower than all other contacts for the fibrillar structure to dominate at equilibrium. Analysis of the species distribution along the aggregation process shows that no other intermediate is ever more populated than the dimer. Instead of a single nucleation event there is a concomitant increase in average aggregate size over the whole system, and the occurrence of multiple parallel processes makes the process more reproducible the larger the simulated system. The sigmoidal shape of the aggregation curves arises from cooperativity among multiple interactions within each pair of peptides in a fibril. A governing factor is the increasing probability as the aggregation process proceeds of neighboring reinforcing contacts. The results explain the very strong bias towards cross β-sheet fibrils in which the possibilities for cooperativity among interactions involving neighboring residues and the repetitive use of optimal side-chain interactions are explored at maximum.

Influence of Aluminium and EGCG on Fibrillation and Aggregation of Human Islet Amyloid Polypeptide

“…It is found in Figure 4(d) that the normalized 1 H NMR integration intensity of aromatic residues in hIAPP within chemical shift from 7.13 to 7.30 ppm was decreased in a typical sigmoidal manner and even no signals were observed after 3 h incubation because the large aggregates were formed. This phenomenon was also observed by other authors for the studies of amyloid fibrillation [47, 48] and amorphous aggregation [49]. The reason is the solidification of protein making the resonance peaks broadened and even covered up in the noise background.…”

Kinetics of Amyloid Aggregation: A Study of the GNNQQNY Prion Sequence

“…Aggregates with a minimal size larger than one show a sigmoid-like growth starting from about the middle of the energy drop, at 5 ns, with an increasing lag time the bigger the species. Sigmoidal aggregation kinetics have been largely observed experimentally [11], [28], [74]–[81] and numerically [82]–[85] and are a well-established characteristic of a nucleated-growth process. Similar cumulative curves have been obtained for Monte-Carlo simulations of large systems of hexapeptides [85] which indicate that the cooperativity between contacts plays a crucial role in the growth and stabilization of all sizes of aggregates.…”

N-Terminal Extensions Retard Aβ42 Fibril Formation but Allow Cross-Seeding and Coaggregation with Aβ42

“…A similar model with kinetic discrimination governing the contacts in a lower free energy structure has previously been used to model protein folding 35 and fibril formation of peptides with only amyloidogenic residues. 36 …”

“…The algorithm for the Monte Carlo simulations is reported elsewhere, 35,36 and in brief it operates as follows. Inter-residue contacts are grouped in two categories, strong and weak contacts, with different average lifetime.…”

“…Each simulation cycle ends by terminating the contacts that expire on that cycle. In an earlier study 36 it was found that 5–20 times longer average survival time for a fibrillar contact ( τ s / τ w = 5–20) is a sufficient criterion for fibrillar structure to dominate at equilibrium, and a value of τ s / τ w = 10 was used in the current simulations. The parameter settings were as follows.…”