Figure 2.

Complexity of reaction network can be significantly reduced by the introduction of moments. To fully describe the aggregation reaction one must account for how all the different sizes of aggregate can interact and inter-convert, leading to a highly complex reaction network with many thousands of possible species and reactions. This network can be enormously simplified by instead considering only the moments of the fibril length distribution, the aggregate number concentration, P, and the aggregate mass concentration, M. While some information about the detailed size distribution is lost in this step, the description of the system in terms of its moments is usually sufficient to fully describe most experimental data and to extract the rate constants of interest: k_n, k₂, k₋, and k+. These are the rate constants of primary nucleation, secondary nucleation, fragmentation, and elongation, respectively. Adapted from Meisl et al. (2017a).