The simulation procedure of FLiSimBA.

The sensor fluorescence lifetime distribution of a FRET-based sensor was modeled as a double exponential decay, as shown in Equation 1 (τ1 = 2.14 ns, τ2 = 0.69 ns) and the lifetimes of photons were sampled with replacement. After the sensor fluorescence was convolved with the probability density function (PDF) of the instrument response function (IRF), the following were added to produce the final simulated data: autofluorescence (autoF) empirically measured from brain tissue with photon number FautoF, afterpulse of the photomultiplier tube (PMT), and background signal (consisting of the dark current of the PMT and light leak) with photon number Fbackground. The histograms of the final simulated data were similar to those of the experimental data. The simulation was repeated 500 times under each P1 and sensor fluorescence photon number (Fsensor) condition. The fitted P1 (based on a double exponential decay fitting of the final simulated data) and empirical lifetime were used for subsequent analyses and evaluations.

Simulated fluorescence lifetime in brain tissue.

(A) Simulated example histograms (upper panels) and heatmaps (middle and lower panels) showing the average fitted P1 and empirical lifetime of the simulated data across a range of P1 and sensor photon number conditions. Fluorescence lifetime histograms were simulated with the sensor only, sensor + autofluorescence (autoF), and sensor + autofluorescence + afterpulse + background (final simulated data).

(B) Summaries of fitted P1 (left) and empirical lifetime (right) with simulated P1 = 0.5. * p < 0.05 vs sensor only; n.s. not significant vs sensor + autoF; # p < 0.05 vs sensor + autoF. Two-way ANOVA with Šídák’s multiple comparisons test.

(C) Empirical lifetime of the simulated and experimental data. P1 and P2 from the fitting of the experimental data were used to generate the simulated data. Note that the mean of the empirical lifetime of the final simulated data is not significantly different from that of the experimental data. * p < 0.05; n.s. not significant; one-way ANOVA with Šídák’s multiple comparisons test.

The data are represented as means and standard deviations.

The minimum number of photons required to detect a specific fluorescence lifetime response.

(A) Schematic illustrating the power analysis used to calculate the minimum detectable difference between two lifetime distributions.

(B-C) Minimum detectable differences in the fitted P1 (B) and empirical lifetime (C) for different numbers of sensor photons and for different numbers of pairs of sampled data (n). The data were simulated with P1 = 0.5.

Comparison of the fluorescence lifetime responses of GaAsP photomultiplier tubes (PMTs) and hybrid detectors (HBDs).

(A) Differences in IRF widths and afterpulse ratios between the GaAsP PMT and HBD. These specific parameters are used in subsequent simulations.

(B) Gaussian IRFs used for simulation, reflecting different Gaussian widths for the GaAsP PMT and HBD.

(C-D) Distributions of the fitted P1 (C) and empirical lifetime (D) of the simulated data from the GaAsP PMT or HBD, with simulated P1 = 0.5 and showing the sensor photon number dependence. The data are represented as means and standard deviations.

(E-F) Minimum detectable difference in the fitted P1 (E) and empirical lifetime (F) for different numbers of sensor photons and different numbers of data samples. The data were simulated with P1 = 0.5.

(G-H) Distribution of the fitted P1 (G) and empirical lifetime (H) of the simulated data from the GaAsP PMT or HBD, with noise introduced from either sampling of photons or sampling from the IRF distribution. The data were simulated without autofluorescence, afterpulse or background and are represented as means and standard deviations.

Impact of the number of sensor photons on the response amplitudes of the fitted P1 and the empirical lifetime.

(A) Schematic illustrating the following question under investigation: in biological systems, as autofluorescence, the afterpulse ratio, and the background remain constant, does the lifetime response change as sensor brightness increases?

(B-C) Distribution of the fitted P1 (B) and empirical lifetime (C) from fluorescence lifetime data with simulated P1 values of 0.4 and 0.5 across different sensor photon numbers. * p < 0.05, P1 = 0.4 vs P1 = 0.5, two-way ANOVA with Šídák’s multiple comparisons test; # p < 0.05, vs photons = 800,000, one-way ANOVA with Dunnett’s multiple comparisons test.

(D-E) Distribution of the changes in the fitted P1 (D) and empirical lifetime (E) for different sensor photon numbers. The simulated P1 varied from 0.4 to 0.5. * p < 0.05, vs photon count = 800,000, one-way ANOVA with Dunnett’s multiple comparisons test.

The data are represented as means and standard deviations.

Conditions needed for the sensor expression-induced lifetime change to be statistically nonsignificant.

(A) Schematic illustrating the question under investigation: as the biological analyte, autofluorescence, afterpulse ratio, and background signals remain constant, as the sensor expression/brightness increases, what is the minimum number of sensor photons needed to tolerate a specific change in sensor expression such that the apparent lifetimes are not significantly different?

(B) Relationship between changes in photon number due to changes in expression level and the minimum number of sensor photons required not to reach statistical significance for both the fitted P1 and empirical lifetime. The data were simulated with P1 = 0.5. The minimum number of sensor photons was calculated by interpolating the intersection between the two curves in (C).

(C) Plots of changes reaching statistical significance according to t tests (calculated as 1.96*standard error of the difference in the mean) and apparent changes due to sensor expression for both the empirical lifetime (upper panels) and fitted P1 (lower panels). The data were simulated with P1 = 0.5. Different sensor expression changes are plotted in each panel.

The data are represented as means and standard deviations.

Impact of no autofluorescence and/or low background on the lifetime dependence of sensor expression.

(A-B) Distribution of the change in fitted P1 (A) and empirical lifetime (B) with different sensor photon numbers, under no autofluorescence, low background, and both improvement conditions. The simulated P1 varied from 0.4 to 0.5. * p < 0.05, vs photon count = 800,000, one-way ANOVA with Dunnett’s multiple comparisons test. The data are represented as means and standard deviations.

(C-D) Relationships between changes in photon number due to expression level and the minimum number of sensor photons required not to reach statistical significance for both the fitted P1 (C) and empirical lifetime (D) under no autofluorescence, low background, or both improvement conditions. The data were simulated with P1 = 0.5.

The orange traces are the same as the corresponding data in Figure 5 and Figure 6, and were reused here for comparison purposes.

Feasibility and parameter requirements for multiplexed fluorescence intensity and lifetime imaging.

(A) Schematic illustrating the motivation for the question. Sensor 1 and sensor 2 are intensity- based sensors with the same color but different fluorescence lifetimes (with single exponential decay constants τ1 and τ2, respectively). The fluorescence signals are combined, and then mathematically deconvolved into individual components. Dotted lines: true fluorescence lifetime histograms of the two sensors; solid lines: simulated fluorescence lifetime histograms with standard deviation (gray shading) before and after deconvolution.

(B) Schematic illustrating the question under investigation: when sensor 1 and sensor 2 change fluorescence intensities and their combined fluorescence is collected simultaneously, can the respective intensities be deconvoluted from the combined measurements?

(C) Deconvoluted number of sensor 1 photons based on different simulated sensor 1 photons. Sensor 2 was simulated with a photon count of 500k. The left and right graphs are based on either 0.5 or 4 ns differences in the single exponential decay constants between the two sensors. The left and right graphs show that the variance in deconvoluted sensor 1 photons is less when the lifetime separation between sensor 1 and sensor 2 is greater. The data are represented as means and standard deviations.

(D) Schematic illustrating the calculation of the statistical power for detecting a specific change in sensor 1 photon counts.

(E) Heatmaps showing the statistical power of detecting specific changes in the intensity of sensor 1 with different sensor 1 baseline photons, different sensor 2 photons, and different lifetime separations between the two sensors. The red line denotes the change in intensity that provides a statistical power of 80%.

(F) Relationship between the minimum detectable intensity change in sensor 1 to reach 80% statistical power and the lifetime difference between the two sensors. Curves were plotted with different sensor 1 baseline photons (left, 500k sensor 2 photons) and different sensor 2 photons (right, 200k sensor 1 baseline photons).

Comparison of the fluorescence decay of sensor fluorescence and autofluorescence.

Fluorescence lifetime histograms of sensor fluorescence and autofluorescence. Note that autofluorescence has lower photon counts and shows faster decay compared with sensor fluorescence.

Minimum detectable intensity change across diverse experimental conditions for multiplexed fluorescence lifetime imaging.

(A) Method of interpolating the minimum detectable intensity change to reach 80% statistical power. Statistical power and sensor 1 intensity change were fitted to a 5-parameter logistic function to calculate sensor 1 intensity change that gives a statistical power of 80%. Data are based on 500k sensor 2 photons, 200k sensor 1 baseline, and 0.5 ns lifetime separation between the two sensors.

(B) Heatmaps showing the minimum detectable intensity change of sensor 1 to reach 80% statistical power, with different sensor 2 photons, sensor 1 baseline, and lifetime separation between the two sensors. Note that minimum detectable intensity change decreases as sensor 2 photons decreases, sensor 1 baseline increases, and lifetime separation increases.

(C) Minimum detectable intensity changes of sensor 1 and sensor 2. Simulation assumed that the two sensors had the same baseline intensity, and both had a dynamic range in intensity that spanned from 1 to 2 fold of the baseline.