A Generic Crystallization-like Model That Describes the Kinetics of Amyloid Fibril Formation

Abstract

Background: Amyloid fibrils are protein aggregates associated with numerous neurodegenerative diseases. Results: A theoretically consistent, two-parameter model is proposed describing very distinct amyloid fibrillization kinetics. Conclusion: Amyloid fibril formation takes place by a general mechanism involving supersaturation-dependent nucleation and growth steps. Significance: This mathematically simple model is expected to be routinely used to characterize the action of new targets for disease therapeutics.

The aggregation of mutant p53 produces prion-like properties in cancer

“…[28][29][30][31] The seeding-nucleation model is not exclusive to PrP fibrillization. A similar model is used to describe the process of crystallization, 32 the polymerization of actin, 33 the assembly of microtubules 34 and the aggregation of amyloid and other proteins. Amyloid formation is known to cause other diseases characterized by similar misfolding processes.…”

What Can the Kinetics of Amyloid Fibril Formation Tell about Off-pathway Aggregation?

“…1b result from the influence of the initial supersaturation on the primary nucleation rate constant k b . Both k a and k b influence the time needed to reach 50% completion (t 50 ) as determined by the following equation (16).…”

“…The parameter k b gives the relative rates of primary nucleation steps over autocatalytic steps. Now that the ability of the CLM to describe traditional fibrillization kinetics (16) and discriminate between true and apparent amyloid inhibitors (17) has been demonstrated, new CLM-based tools are hereby proposed in order to identify off-pathway processes. However, a preliminary note is required to define the regular kinetic behaviors expected in the absence of parallel aggregation.…”

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.…”