Fig 1.
(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 (Sact = 0). The correlated line (red line) indicates states in which average rates of back and forth reactions are balanced as kf(t)Sact = kb(t)Sinact. The moving lines (black dotted arrows) indicate trajectories with varying Sact. The gray scatter dots represent the typically observed relationship between Fi and Fa in the FRET imaging. (B) The lengths of the orange and purple arrows, do and dc, represent measures proportional to Sact and Stot. (C) The orange and pink right triangles have geometric similarity. The length of the perpendicular line, , is proportional to do and Sact. The length of the purple arrows,
, can be approximated when the state (Fi, Fa) is closely located along the correlated line. The LP measure is calculated by
. (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, kf(t) and kb(t), fluctuated in time. These data were generated by an OU process.(B) Simulation result of Sact and Sinact. (C) Sact and Sinact in (A) were converted to Fa and Fi 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 Fa and Fi, obtained by iterating the simulations and varying total amount of biosensor, Stot. The blue and red lines indicate the inactive line and the correlated line. (D) The black markings indicate the grand truth of Sact/Stot, 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 Sact/Stot. (E) The dependencies of the ratiometric, LP and HC measures on Sact/Stot. The HC measure responded within a dynamic range of Sact/Stot 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.