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. Author manuscript; available in PMC: 2016 Mar 12.
Published in final edited form as: FEBS Lett. 2015 Jan 31;589(6):672–679. doi: 10.1016/j.febslet.2015.01.032

Table 1.

Consequences for Amyloid Kinetics of Parameter Changes within the Nucleation-Growth Model

Parameter# Consequences*
Monomer concentration (M)

  1. An increase in monomer concentration leads to an increase in the rate and extent of amyloid formation (weight concentration) [3,7,8,11,21–23,28].

  2. An increase in monomer concentration can either increase or reduce the initial amyloid size distribution depending upon its relative effect on nucleation and growth rates [21,22].
Nucleation rate (kn+, kn−)

  1. For situations limited to the NG model i.e. intrinsic rate of nucleus formation ≪ intrinsic rate of amyloid formation, or alternatively, equilibrium extent of nucleus formation ≪ extent of amyloid, an increase in nucleation rate will increase the rate of amyloid formation (weight concentration). Beyond this regime the rate and extent of amyloid formation can decrease in response to a large amount of nucleus production [21,22].

  2. An increase in the nucleation rate will lead to a general shortening of the amyloid size distribution – note this conclusion can be affected by other parameters such as the fiber joining rate and the fiber fragmentation rate [21,22,23].
Nucleation size (n) In the classical Oosawa-Asakura model of helical polymer formation [7], an increase in the molecularity^ of the nucleation reaction will lower the concentration of the critical nucleus. This will concomitantly

  1. slow the rate of amyloid formation (weight concentration) [21,22]

  2. increase the size distribution of amyloid (average molecular weight) [21,22]
Growth rate by monomer addition (kg+) Increasing the rate of monomer addition to amyloid fibrils will tend to (1) increase the rate of amyloid formation (weight concentration) [8,21]
(2) increase the size distribution of amyloid (average molecular weight)
Dissociation rate by monomer loss (kg−) Slower rates of monomer dissociation from amyloid fibrils will tend to

  1. increase the rate of amyloid formation (weight concentration)

  2. increase the size distribution of amyloid (average molecular weight)
Fiber breakage rate (kb) Fiber breakage rates have been shown to display different behaviors.

  1. At low breakage rates (relative to total amyloid growth rate) increases in breakage rate will lead to a net increase in amyloid growth rate. At high fiber breakage rates (relative to the total amyloid growth rate) further increases in fiber breakage rate lead to a dissolution of amyloid fibers and a massive shortening of the fiber distribution [8,10,21,23].

  2. Increases in fiber breakage rate always tend towards a shortening of the amyloid size distribution [8,10,21,23].
Fiber joining rate (kj) The effect of variation in fiber joining rate on both the rate of amyloid formation and the amyloid fiber distribution properties has been less well studied [9,10]. Intuitively, we may propose that increasing the fiber joining rate will,

  1. decrease the total rate of amyloid formation

  2. increase the amyloid size distribution
#

Parameters refer to rate constants governing the elementary steps of the nucleated growth scheme shown (Eqn. 1).

*

Here we draw a distinction between two types of amyloid growth. The first refers to the total mass of monomer incorporated into amyloid i.e. weight concentration. The second refers to the general size of the amyloid size distribution i.e. average molecular weight [8,22,23].

^

By molecularity we mean the number of molecules involved in the reaction.