FRET efficiency image

Estimate FRET efficiencies in an image using a phasor-based model.

Förster resonance energy transfer (FRET) is a distance-dependent interaction between two luminescing molecules where energy is transferred from a donor to an acceptor molecule. FRET efficiency is sensitive to donor-acceptor distances, making it useful for studying molecular interactions.

The phasor_from_fret_donor() function is used to calculate a theoretical FRET efficiency trajectory and the phasor_nearest_neighbor() function is then used to estimate the FRET efficiencies of measured phasor coordinates in an image from the trajectory.

Import required modules, functions, and classes:

import numpy

from phasorpy.datasets import fetch
from phasorpy.filter import phasor_filter_median, phasor_threshold
from phasorpy.io import phasor_from_simfcs_referenced
from phasorpy.lifetime import phasor_from_fret_donor, phasor_to_normal_lifetime
from phasorpy.phasor import phasor_nearest_neighbor
from phasorpy.plot import (
    PhasorPlot,
    plot_histograms,
    plot_image,
    plot_phasor_image,
)

Read dataset

Read phasor coordinates from the LFD workshop dataset, containing fixed samples of CFP and CFP-YFP expressing cells. The data were acquired using a Lambert frequency-domain FLIM instrument at 80 MHz. The phasor coordinates are already referenced:

filename = 'CFP and CFP-YFp.ref'
frequency = 80.0  # MHz

mean, real, imag, attrs = phasor_from_simfcs_referenced(fetch(filename))

plot_phasor_image(mean, real, imag, title=filename)

Filter the phasor coordinates and set the intensity threshold to 9000 counts to remove low-intensity background pixels:

mean, real, imag = phasor_filter_median(mean, real, imag, repeat=2)
mean, real, imag = phasor_threshold(
    mean, real, imag, mean_min=9000, real_min=0, imag_min=0, open_interval=True
)

FRET efficiency trajectory

Calculate the theoretical FRET efficiency trajectory in phasor space for the CFP FRET donor. The trajectory represents the path phasor coordinates follow as FRET efficiency increases from 0% (donor only) to 100% (complete energy transfer). The trajectory is a model: it depends on the estimated donor-only phasor (assumed single exponential), the background phasor, and fixed assumptions about the fraction of donors undergoing FRET and the background contribution. Different choices change the trajectory and the estimated efficiencies:

donor_real, donor_imag = 0.72, 0.45  # estimated pure CFP phasor coordinates
background_real, background_imag = 0.6, 0.41  # estimated background phasor

fret_efficiency_range = numpy.linspace(0.0, 1.0, 100)
donor_lifetime = phasor_to_normal_lifetime(donor_real, donor_imag, frequency)

fret_trajectory = phasor_from_fret_donor(
    frequency,
    donor_lifetime,
    fret_efficiency=fret_efficiency_range,
    donor_fretting=1.0,  # all donor molecules can undergo FRET
    donor_background=0.1,  # 10% background signal contribution
    background_real=background_real,
    background_imag=background_imag,
)

phasor_plot = PhasorPlot(
    frequency=frequency,
    xlim=(0.5, 1),
    ylim=(0.2, 0.6),
    title='FRET efficiency trajectory',
)
phasor_plot.hist2d(real, imag)
phasor_plot.line([donor_real, background_real], [donor_imag, background_imag])
phasor_plot.plot(
    donor_real,
    donor_imag,
    'o',
    color='tab:green',
    markeredgecolor='black',
    markersize=10,
    zorder=10,
    label='Donor only',
)
phasor_plot.plot(
    background_real,
    background_imag,
    'o',
    color='black',
    markersize=10,
    zorder=10,
    label='Background',
)
phasor_plot.plot(
    *fret_trajectory,
    '-',
    color='tab:orange',
    linewidth=4,
    alpha=0.8,
    label='FRET trajectory',
)
phasor_plot.show()

Estimate FRET efficiency

Estimate FRET efficiencies for each pixel in the image by finding the nearest point on the FRET efficiency trajectory to each measured phasor coordinate. Every valid pixel is assigned an efficiency on the trajectory, even if its phasor coordinates are not well described by the model:

fret_efficiencies = phasor_nearest_neighbor(
    real,
    imag,
    *fret_trajectory,
    values=fret_efficiency_range,
    dtype=real.dtype,
    num_threads=4,  # use multiple threads for faster computation
)

Visualize the spatial distribution of FRET efficiencies:

plot_image(fret_efficiencies, title='Estimated FRET efficiency')

Visualize the distribution of FRET efficiencies as a histogram:

plot_histograms(
    fret_efficiencies * 100,  # convert to percentage
    range=(0, 35),
    bins=35,
    xlabel='FRET efficiency (%)',
    ylabel='Counts',
    title='FRET efficiency histogram',
)

Conclusions

The estimated FRET efficiencies are conditional on the trajectory model and its assumptions. Within that model, the FRET efficiency image shows spatial heterogeneity in donor-acceptor interactions across the sample. Higher FRET efficiencies are consistent with closer proximity between CFP and YFP molecules. Lower FRET efficiencies may indicate cells expressing primarily CFP donor without acceptor, or regions where CFP and YFP are too far apart for efficient energy transfer. They may also result from a smaller fraction of donors undergoing FRET, an effect the fixed model cannot distinguish from lower FRET efficiency. The histogram shows the distribution of model-based efficiency estimates in the population. Biological interpretation should consider the sensitivity of these estimates to the model assumptions, for example by validating them with control samples.