  Many different proteins self-aggregate into insoluble fibrils growing
apically by reversible addition of elementary building blocks. But beyond this
common principle, the modalities of fibril formation are very disparate, with
various intermediate forms which can be reshuffled by minor modifications of
physico-chemical conditions or amino-acid sequences. To bypass this complexity,
the multifaceted phenomenon of fibril formation is reduced here to its most
elementary principles defined for a linear prototype of fibril. Selected
generic features, including nucleation, elongation and conformational
recruitment, are modeled using minimalist hypotheses and tools, by separating
equilibrium from kinetic aspects and in vitro from in vivo conditions. These
reductionist approaches allow to bring out known and new rudiments, including
the kinetic and equilibrium effects of nucleation, the dual influence of
elongation on nucleation, the kinetic limitations on nucleation and fibril
numbers and the accumulation of complexes in vivo by rescue from degradation.
Overlooked aspects of these processes are also pointed: the exponential
distribution of fibril lengths can be recovered using various models because it
is attributable to randomness only. It is also suggested that the same term
"critical concentration" is used for different things, involved in either
nucleation or elongation.
