Nucleation of amyloid fibrils

Abstract

We consider nucleation of amyloid fibrils in the case when the process occurs by the mechanism of direct polymerization of practically fully extended protein segments, i.e. -strands, into -sheets. Applying the classical nucleation theory, we derive a general expression for the work to form a nanosized amyloid fibril (protofilament) constituted of successively layered -sheets. Analysis of this expression reveals that with increasing its size, the fibril transforms from one-dimensional into two-dimensional aggregate in order to preserve the equilibrium shape corresponding to minimal formation work. We determine the size of the fibril nucleus, the fibril nucleation work and the fibril nucleation rate as explicit functions of the concentration and temperature of the protein solution. The results obtained are applicable to homogeneous nucleation which occurs when the solution is sufficiently pure and/or strongly supersaturated.

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.…”

Communication: Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules

“…This peculiar behaviour is a departure from the classical behaviour predicted by CNT. The transition values correspond with those predicted by Kashchiev et al 20,22 for jumps in the solubility of amyloid fibril, where each supersaturation region is defined by the number of rows a cluster requires in order to grow irreversibly. A general formula for the transition supersaturations can be derived; 20 S i = 2ψ y /i where i is the number of rows in a cluster, a row being defined as growth in the strong bonding direction, x.…”

“…The transition values correspond with those predicted by Kashchiev et al 20,22 for jumps in the solubility of amyloid fibril, where each supersaturation region is defined by the number of rows a cluster requires in order to grow irreversibly. A general formula for the transition supersaturations can be derived; 20 S i = 2ψ y /i where i is the number of rows in a cluster, a row being defined as growth in the strong bonding direction, x. Above each S i a cluster with i rows can grow irreversibly, hence above S 1 = 2ψ y /1 = 2 all clusters with one row can grow to macroscopic size, which defines this region as the metanucleation range, where each single molecule acts as a nucleus and hence nucleation is instantaneous.…”

“…Recent computational and theoretical research has shown that introducing anisotropy into the interactions between molecules creates ambiguity, changing the well defined nucleus size to a distribution of nucleus sizes. 21,22 The resultant change to the nucleation mechanism has been shown to affect the solubility of clusters, 20 crystal nucleation rate, 26 and nucleation pathway. 3 Here, we directly measure the distribution of nucleus sizes, characterise the dependence on the interaction anisotropy and supersaturation, and relate this to the nucleus shape to explain the peculiar behaviour of n*.…”

“…[19][20][21][22][23][24] The propensity for a macroscopic crystal to nucleate can be characterised by the nucleus size, n* (also known as the critical nucleus size), the size a growing cluster must surpass to be more likely to grow than dissolve. According to classical nucleation theory (CNT) 25 in a single component system, there exists a well defined n* at the cluster size which requires maximal work for its formation.…”