A Three-Stage Kinetic Model of Amyloid Fibrillation

Abstract

Amyloid fibrillation has been intensively studied because of its association with various neurological disorders. While extensive time-dependent fibrillation experimental data are available and appear similar, few mechanistic models have been developed to unify those results. The aim of this work was to interpret these experimental results via a rigorous mathematical model that incorporates the physical chemistry of nucleation and fibril growth dynamics. A three-stage mechanism consisting of protein misfolding, nucleation, and fibril elongation is proposed and supported by the features of homogeneous fibrillation responses. Estimated by nonlinear least-squares algorithms, the rate constants for nucleation were approximately 10,000,000 times smaller than those for fibril growth. These results, coupled with the positive feedback characteristics of the elongation process, account for the typical sigmoidal behavior during fibrillation. In addition, experiments with different proteins, various initial concentrations, seeding versus nonseeding, and several agitation rates were analyzed with respect to fibrillation using our new model. The wide applicability of the model confirms that fibrillation kinetics may be fairly similar among amyloid proteins and for different environmental factors. Recommendations on further experiments and on the possible use of molecular simulations to determine the desired properties of potential fibrillation inhibitors are offered.

Kinetic theory of amyloid fibril templating

“…3 In particular, the kinetics of fibril formation have been extensively studied [4][5][6][7][8][9] to understand the stochasticity of disease onset and the lifetimes of metastable states that are thought to play a role in disease progression. 10 These kinetics are difficult to study because the timescales for disease progression, typically years to decades, are prohibitive for direct biophysical studies under physiological conditions.…”

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

“…They tend to assemble as toxic fibrillar structures, which may in turn associate into mature amyloid inclusions. Several mathematical models have been proposed to explain the protein aggregation process in ND: Stochastic nucleation and fibril dynamics, for instance, have been modelled using a two‐step reaction mechanism 42, 43, 44, 45, 46, 47 and validated with empirical data 48.A micelle intermediate on the pathway of protein aggregation has been described using mathematical models 49, 50.Furthermore, models of inhibiting end‐blocking drugs have also been formulated for describing the protein aggregation process 51, 52, 53. …”

“…Stochastic nucleation and fibril dynamics, for instance, have been modelled using a two‐step reaction mechanism 42, 43, 44, 45, 46, 47 and validated with empirical data 48.…”

Amyloid Polymorphism of α-Synuclein Induced by Active Firefly Luciferase

“…Once nucleus forms during the lag phase, the fibrillar growth is drastically accelerated through selective accretion of the monomeric protein to the nucleus as they experience structural transition to an amyloidogenic conformation. [5][6][7] Therefore, the nucleus formation is not only the rate-determining step of entire fibrillation process, 8 but it also determines eventual properties of amyloid fibrils such as fibrillar morphology, stability, and possible toxicity. [9][10][11][12][13] -Synuclein is a natively unfolded acidic protein with M r of 14 kDa that is primarily found at pre-synaptic terminals.…”