Figure 5. Schematic plot of a fluorescence signal.

Initially, for times t smaller than a transient time θ, called the lag time, no fibrils are observed. After θ, the fluorescence signal I_F increases with time and flattens out at later times because of the decrease of the concentration of proteins in the solution. The aggregation rate is usually taken to be the slope of I_F in the linear regime: $I_S^{\exp }=\Delta I_F\left(t\right)∕\Delta t$ (indicated by the red dashed line), and the lag time θ is determined by the extrapolation to zero of the red dashed line. In the inset, we illustrate the effect of a change in the barrier for elongation on the total number of oligomers, N(t), formed in the solution. The solid lines are based on the analytical expression of Kashchiev (1969) and the dashed lines describe their long-time behavior based on Eq. 2. The values for the barriers for elongation are: ΔF_e∕kT^*=0 (black), 1 (red), 2 (green), and 3 (blue), while all other parameters are unchanged. The unit time is set to be the lag time θ₀ for ΔF_e=0. In CNT, the steady-state nucleation rate is defined by: $I_S^{CNT}=\Delta N\left(t\right)∕\Delta t$, and $I_S^{CNT}$ and θ are determined, as in the experimental case, by the slope of the red dashed line and its extrapolation to zero, respectively. Hence, $I_S^{\exp }$ and $I_S^{CNT}$ can be compared qualitatively.