Two New FRET Imaging Measures: Linearly Proportional to and Highly Contrasting the Fraction of Active Molecules

Abstract

We developed two new FRET imaging measures for intramolecular FRET biosensors, called linearly proportional (LP) and highly contrasting (HC) measures, which can be easily calculated by the fluorescence intensities of donor and acceptor as a ratio between their weighted sums. As an alternative to the conventional ratiometric measure, which non-linearly depends on the fraction of active molecule, we first developed the LP measure, which is linearly proportional to the fraction of active molecules. The LP measure inherently unmixes bleed-through signals and is robust against fluorescence noise. By extending the LP measure, we furthermore designed the HC measure, which provides highly contrasting images of the molecular activity, more than the ratiometric measure. In addition to their advantages, these measures are insensitive to the biosensor expression level, which is a fundamental property of the ratiometric measure. Using artificial data and FRET imaging data, we showed that the LP measure effectively represents the fraction of active molecules and that the HC measure improves visual interpretability by providing high contrast images of molecular activity. Therefore, the LP and HC measures allow us to gain more quantitative and qualitative insights from FRET imaging than the ratiometric measure.

Fig 1. FRET biosensor.

(A) Schematic of the structure of the intramolecular FRET biosensor, which consists of the studied protein (sensor domain) fused with a ligand domain, which is sandwiched by the donor and acceptor fluorophores, e.g., cyan fluorescent protein (CFP) and yellow fluorescent protein (YFP). The distance between the donor and the acceptor depends on the conformation, i.e., active or inactive state, of the focused protein. In the inactive state, the CFP is excited and emits fluorescence with a specific wavelength, whereas in the active state, FRET occurs due to the close proximity between the CFP and the YFP, and the YFP emits fluorescence with a different wavelength. (B) Normalized excitation and fluorescence spectra of the donor and acceptor fluorophores are shown. The CFP emission spectrum largely overlaps with the YFP excitation, enabling FRET. The blue, cyan and yellow shaded regions indicate the light wavelengths for CFP excitation, CFP emission filtering and YFP emission filtering, respectively. The blue and yellow regions represent cross-excitation and bleed-through.

Fig 2. Phase space between the fluorescence from the donor and acceptor.

(A) The inactive line (blue line) indicates states in which all biosensors are in the inactive state (S_act = 0). The correlated line (red line) indicates states in which average rates of back and forth reactions are balanced as k_f(t)S_act = k_b(t)S_inact. The moving lines (black dotted arrows) indicate trajectories with varying S_act. The gray scatter dots represent the typically observed relationship between F_i and F_a in the FRET imaging. (B) The lengths of the orange and purple arrows, d_o and d_c, represent measures proportional to S_act and S_tot. (C) The orange and pink right triangles have geometric similarity. The length of the perpendicular line, ${\widehat{d}}_o$, is proportional to d_o and S_act. The length of the purple arrows, ${\widehat{d}}_c$, can be approximated when the state (F_i, F_a) is closely located along the correlated line. The LP measure is calculated by ${\widehat{d}}_o/{\widehat{d}}_c$. (D) Black lines were determined by the lower and upper ratiometric activity bounds. The states can be decomposed using two basis vectors along these black lines (dark blue and red arrows). The HC measure is calculated by a ratio between these factors.

Fig 3. Application of the measures to artificially generated data.

(A) In a simulation, the reaction rates of the biosensor, k_f(t) and k_b(t), fluctuated in time. These data were generated by an OU process.(B) Simulation result of S_act and S_inact. (C) S_act and S_inact in (A) were converted to F_a and F_i in an observation process through two fluorescence channels with the bleed-through (Eqs 1 and 2) and indicated by the yellow line. The gray scatter dots indicate the distribution of F_a and F_i, obtained by iterating the simulations and varying total amount of biosensor, S_tot. The blue and red lines indicate the inactive line and the correlated line. (D) The black markings indicate the grand truth of S_act/S_tot, whereas the green, red and blue lines indicate the ratiometric, LP and HC measures, respectively. The amplitudes of these measures are normalized to minimize square errors from S_act/S_tot. (E) The dependencies of the ratiometric, LP and HC measures on S_act/S_tot. The HC measure responded within a dynamic range of S_act/S_tot in (D), which is indicated by the black arrow and shaded region. Each measure was normalized so that the maximum value is 1.

Fig 4. Experimental data of FRET imaging.

(A, B) Snapshot images of the migrating cell expressing the biosensor Raichu–Cdc42. Images of the ratiometric measures are presented with those of the LP (A) and HC (B) measures in heat maps with the same range for comparison. (C) Intracellular distributions of the ratiometric, LP and HC measures along the black lines in A and B. (D) Image contrast was quantitatively evaluated using relative standard deviation (RSD), relative mean absolute error (RMAE), and Michelson contrast (MC). The error bars indicate the standard error. Significant differences are indicated (**p<0.01, *p<0.03; Mann-Whitney U test). These contrast measures at individual samples (cells) were provided in S1 Table.