Dissecting the Kinetic Process of Amyloid Fiber Formation through Asymptotic Analysis

Abstract

Amyloids are insoluble fibrous protein aggregates which, when abnormally accumulated in the body, can result in amyloidosis and various neurodegenerative diseases. In this work, we describe a new approach to the asymptotic solution of the master equation of amyloid fiber aggregations. It is found that four distinct and successive stages (lag phase, exponential growth phase, breaking phase and static phase) dominate the fiber formation process. Based on the distinctive power-law dependence of the half-time and apparent growth rate of the fiber formation on the initial protein concentration, we propose a novel classification for amyloid proteins theoretically.

Structural Biology of Calcitonin: From Aqueous Therapeutic Properties to Amyloid Aggregation

“…Work by Arvinte and colleagues provided one of the first studies focused on the structure and kinetics of hCT fibrillation . Arvinte found higher peptide concentrations correlate with decreased lag time, a behavior that has been reproducibly observed for sCT, hCT, and other amyloids, both experimentally and in simulations ,. hCT also showed a propensity to form well‐ordered fibrillar aggregates, another common characteristic of other amyloidogenic sequences (Figure ) ,,.…”

Statistical Mechanics and Kinetics of Amyloid Fibrillation

“…The kinetic modeling of conformational pre-conversion is most straightforward. All terms concerning instantaneous monomer concentration m(t) in previous models should be replaced by a new concentration of monomers in the unfolded (or partially unfolded) state m u (t) as required by the fibrillar structure [127].…”

“…The former section is wholly based on macroscopic kinetic models for the mass concentration and number concentration of fibrils, but why we can adopt this simple picture and how its accuracy is compared to models at a molecular Image is taken from [127] with copyright permission.…”

“…At last, we want to introduce the half time of fibrillation t 1/2 and the apparent fiber growth rate k app [127], i.e.…”

Modeling fibril fragmentation in real-time

“…Even for bundled fibrils in vivo, fragmentation is unavoidable in the presence of mechanical stress, thermal motion, or chaperones such as Hsp104, which has a known ability to fragment fibril samples [10]. Actually as a special kind of secondary nucleation, fragmentation can effectively accelerate the fiber formation process by providing new seeds [11], affect the scaling relations between kinetic quantities (like the lag-time and maximum fiber growth rate) and protein concentration (from critical-nucleus-size dependent to independent) [12], alter the detailed fiber length distribution from exponentially decaying to bell-shape-like [13], and even enhance the toxicity of fibril samples to disrupt membranes and to reduce cell viability [14].To quantify the key role of fragmentation played during the formation of breakable amyloid fiber, various experiments, like the shear flow [15,16] and sonication studies [17,18], are designed. However to interpret the experimental results, especially to provide a quantitative relationship between the observed data and their underlying mechanisms, is not an easy task.…”