  The formation and proliferation of protein aggregates play a central role in
a number of devastating neuro-degenerative diseases. Many experimental studies
indicate that the ability of existing aggregates to replicate is a key property
in generating their pathogenic effect across a range of diseases. However,
given the complexity of the process in vivo, no principled general approach
currently exists to obtain the rates of the fundamental steps that underlie
aggregate formation from measurements in living systems. In order to address
this challenge, here we present a general approach for analysing aggregation
kinetics that considers broad classes of processes that can be described by a
family of scaling solutions. Our approach is not limited only to fibrillar
aggregates, but applies to any aggregate shape. We show that the rates can
reliably be extracted by fitting of a simple logistic function, even from
experimental data in living systems, and give a very general analytical
expression that relates the scaling of the exponential rate with monomer
concentration to the microscopic details of the underlying reaction. This
approach can thus be used to infer the microscopic mechanism driving the
aggregation process from macroscopic measurements in complex systems.
