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Data were fitted by nonlinear least squares, using Fitall (MTR software, Toronto, Canada) modified with an exponential fitting function.
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The exponential fitting function provides a means to statistically and mathematically determine the best fit for the binding between Aβ and the membranes, and provides a more sophisticated fitting procedure that can distinguish curves that do not follow the simple bimolecular binding.
The model with the bi-exponential fitting function calculated the values with slightly higher precision than that with a mono-exponential fitting function (R[mono] = 0.965 ± 0.144; R[bi] = 0.996 ± 0.131).
The compliance method is used to determine the energy release rate but with a specific formula where an exponential fitting is preferred instead of the power classical fitting.
A bi-exponential model to fit the curves reported in Fig. 2b and c can be ruled out because previous in vitro studies [20, 21], testing bi-exponential fitting functions in T2 decays, demonstrated a negligible component with a very short time constant and a predominant component with a time constant comparable to the mono-exponential fitting relaxation time.
Therefore, as a nonlinear fitting function, the exponential function was selected.
A local fitting function is constructed and then curvature can be calculated analytically from the fitting function.
A single exponential fitting can be used to get the PL lifetime (τPL).
The RMSE of the responsivity function linear fitting was very small; however, exponential fitting produced a better fit (Table 1) and the difference of the fits was small.
1) Fit an exponential to each function.
where and is an exponential integral function.
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