Table 1.

Testing whether the condition from Eq. 10 is consistent with the kinks observed in the experimental data of Fig. 1

Description	Insulin	Lysozyme	β2 microglobulin
mtot at kink (from Fig. 1)	160 μM	300 μM	40 μM
κ from kinetic fit (9,14)	1.3 × 10−4 s−1	1.2 × 10−3 s−1	7.2 × 10−5 s−1
k+ from insulin kinetic fit (14)	5 × 104 M−1 s−1	5 × 104 M−1 s−1	5 × 104 M−1 s−1
V	100 μL	100 μL	100 μL
M∗/mtot	0.1	0.1	0.1
Solution for kn for nc = 1	5.2 × 10−22 M−1 s−1	2.3 × 10−21 s−1	1.2 × 10−21 s−1
Solution for kn for nc = 2	6.4 × 10−18 M−1 s−1	1.6 × 10−17 M−1 s−1	5.8 × 10−17 M−1 s−1
Solution for kn for nc = 3	1.2 × 10−13 M−1 s−1	1.6 × 10−13 M−1 s−1	4.4 × 10−12 M−1 s−1
Average time to nucleus $=n_c!/\left[k_n{m}_{\text{tot}}^{n_c}{N}_{A}V\right]$	56 h	7 h	98 h
Predicted lag time at kink	112 h	13 h	197 h
Lag time at kink (from Fig. 1)	∼25 h	∼20 h	∼10 h

rows 2–6 show the parameter values used. Rows 7–9 show the resulting values of the nucleation rate constant k_n from numerical solution of Eq. 10, for n_c = 1, n_c = 2, and n_c = 3. Rows 10–12 show the implied predictions for the time to formation of the first nucleus and the lag time at the kink. The latter is compared to the experimental value extracted from Fig. 1. Values of κ were extracted from the gradient of the steepest part of the growth curves. Those shown here are the means, for each protein, at the protein concentration where the kink occurs.