Monte Carlo simulations of isotropic <i>κ</i>²

<p><b>distribution. A.</b> Cartoon illustrating how the dipole orientation factor <i>κ</i>² is based on 2 angles, <i>θ</i> and <i>ω</i> (see Eq 6). <b>B.</b> Monte Carlo simulation of the <i>κ</i>² probability distribution assuming that <i>θ</i> and <i>ω</i> are randomly distributed (isotropic). Note that the mode of this distribution is 0 and the average is 2/3.</p

For the same separation distance, dynamic and static isotropic regimes have different FRET efficiency distributions and decays.

<p><b>A.</b> The FRET efficiency distributions from Gaussian populations with a mean <i>R_DA</i> value of 5.4 nm±1% in either the dynamic random isotropic reorientational regime (<i>κ</i>² = 2/3, GRAY peak) or the static random isotropic orientational regime (BLUE bimodal distribution). <b>B.</b> Fluorescence decays for the populations depicted in panel A. <b>C.</b> The dependence of 〈<i>E</i>〉 on <i>R_DA</i> in these dynamic (GRAY open circles) and static (BLUE squares) regimes. The blue area between these curves depicts the region between the dynamic and static regimes into which the FRET efficiencies for samples that have rotational correlation times similar to the inverse of the energy transfer rates will fall. <b>D</b> and <b>E.</b> FRET efficiency distributions (probability densities, <i>p(E)</i>) used to generate the dynamic (D) or static (E) average FRET efficiency curves displayed in panel C. Note that in the static random isotropic regime, samples tend to have FRET efficiencies either near 0% or centered at <i>F</i>/(1+<i>F</i>). <b>F.</b> FRET efficiency distributions, <i>p(E)</i>, for fixed separation ranging from 1 to 10 nm and a Förster separation of 5.4 nm (<i>F</i>-values ranging from 3.7×10⁴ to 3.7×10⁻²) calculated analytically.</p

The donor fluorescence decay is an indicator of the distribution of FRET efficiency values in a population. A.

<p>Simulated distribution of FRET efficiencies for a narrow normally distributed <i>R_DA</i> population, <b>〈</b><i>E</i><b>〉</b> = 0.5. <b>B.</b> Simulated distribution of FRET efficiencies for a bimodal population with E = 0 & 1. <b>C.</b> Fluorescence decays from the populations depicted in panels A and B. For comparison the decay of donors in the absence of acceptors is also plotted (Black trace). Note that the decay of the population depicted in panel B (RED trace) was poorly fit by a single exponential decay model (dotted line), but was well fit using a double exponential decay model (dashed and dots line).</p

Large variance in separation (<i>R_DA</i>) produces bimodal FRET efficiency probability density histograms, multi-exponential decays, and alters the FRET efficiency from that pertaining to the mean separation.

<p><b>A.</b> A histogram of <i>R_DA</i> values from 5 Monte-Carlo simulations, each having a Gaussian distribution with its mode at 5.4 nm, but with standard deviations ranging from 1 to 200% of the mode. Note that points with negative separation were dropped from the distribution in the simulation. <b>B.</b> The distribution of FRET efficiency probabilities from the populations depicted in panel A. The <i>R</i>₀ value was set to 5.4 nm, the lifetime of the donor in the absence of acceptors was set to 3 ns, and <i>κ</i>² was set to 2/3 to simulate the dynamic random isotropic reorientational regime. green tinted area represents <i>E</i><0.05, and the yellow tinted area represents <i>E</i>>0.95. These points corresponded to the <i>R_DA</i> values in panel A with similar tints. <b>C.</b> Fluorescence decays from the populations depicted in panel A. D. The <i>R</i>₀ normalized dependence of 〈<i>E</i>〉 on both <i>R_DA</i> and its variance.</p

Long-lived acceptor dark states can produce bimodal FRET efficiency distributions, multi-exponential donor excited-state decays, and a decrease in measured average FRET efficiency compared with that for the mean separation.

<p><b>A.</b> Long-lived dark states (blinking and flickering) in donor and/or acceptor fluorophore populations may attenuate the apparent <i>R</i>₀ value for FRET, in the former by reducing the measured quantum yield, in the latter by reducing the measured extinction coefficient and thereby the spectral overlap integral. The attenuation factor () is plotted as a function of dark donor fraction (<i>f_Dd</i>) and dark acceptor fraction (<i>f_Ad</i>). <b>B.</b> Monte-Carlo simulations were used to model the distribution of FRET efficiencies from populations with 0 to 50% acceptor dark states. Separations were modeled using a Gaussian with a standard deviation equal to 1% of the mode. The true <i>R</i>₀ was fixed for all samples at a value of 5.4 nm, the lifetime of the donor in the absence of acceptors set to 3 ns, <i>κ²</i> set to 2/3, and it was assumed that dark states do not absorb in the region of donor emission. <b>C.</b> Fluorescence decays for the populations depicted in panel B. <b>D.</b> Dependence of measured 〈<i>E</i>〉 on the ratio of fixed (i.e., no distribution width) <i>R_DA</i> to true <i>R</i>₀ and the fraction <i>f_Ad</i> of acceptors in the dark state.</p

FPFA of V-CaMKIIα expressed in HEK cells.

<p>(A) Average TRA for V-CaMKIIα (Black) holoenzyme in cells. TRA traces for Venus monomers (V1, Yellow) and Venus trimers (V3, Green) expressed in HEK cells are also plotted as a reference, and to illustrate that the Venus-tagged catalytic domains in V-CaMKIIα produce an anisotropy signal most consistent with Venus-dimers. The excitation power used was 6 mW. (B) The brightness values for V1–V6 expressed and measured in HEK cells are plotted as a function of the number of Venus molecules in each construct. Each point represents a single cell, and at least 3 cells were measured for each Venus concatemer. Note that the V1 brightness was slightly elevated, presumably due to endogenous autofluorescence. Red dashed line indicates fit to a linear model for V2–V6 with dashed blue lines indicating the 95% confidence bands. The average brightness and normalized brightness of V-CaMKIIα (Blue squares, mean±SD, n = 11 cells) is plotted on the main graph with error bars indicating two standard deviations.</p

Fluorescence Polarization and Fluctuation Analysis: A method for studying the structure of protein complexes.

<p>(A) Six possible structures for a hypothetical protein (Blue hexagon) tagged with Venus (yellow cylinder). Example 1 depicts monomers. Examples 2 and 3 depict dimers. Attached Venus molecules are in close apposition for example 2 but not for example 3. Examples 4 and 5 depict hexamers. Pairs of attached Venus molecules are in close apposition for example 4 but not for example 5. Example 6 depicts monomers that are confined to a sub-compartment (dashed line) where they are expressed at a high concentration. (B) Schematic for microscope to measure FPFA. (C) Micro-time data measured for a homogenate prepared from cells expressing Venus monomers are used to calculate fluorescence lifetime histograms for photons detected by either the parallel or perpendicular hybrid-detectors as a function of time after the laser excitation pulse (left panel). These two decay curves are then used to calculate the time-resolved anisotropy (right panel top), or fluorescence lifetime (right panel bottom) of Venus monomers. Red dashed lines show fitting to a single exponential model. (D) Macro-time data measured for a homogenate prepared from cells expressing Venus monomers are used to calculate auto- and cross-correlation functions for photons detected in the parallel and perpendicular hybrid-detectors. A single diffusible-component 3-D Gaussian model was used to fit the cross-correlation (red dashed line), and to estimate the correlation time and the average number of molecules in the observation volume. The excitation power used was 10.2 mW.</p

FPFA of CaMKIIα holoenzyme.

<p>(A) The normalized brightness for V-CaMKIIα holoenzyme, and mutant that cannot bind Ca²⁺/CaM. Bars represent the means with n = 5. The excitation power used was 10.2 mW. (B) The correlation times for samples in panel A. (C) Average TRA for samples in panel A. TRA traces for Venus monomers (V1) and Venus trimers (V3) from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0038209#pone-0038209-g002" target="_blank">figure 2B</a> are overlaid as a reference, and to illustrate that the Venus-tagged catalytic domains in V-CaMKIIα produce an anisotropy signal most consistent with Venus-dimers. (D) Hetero-FRET analysis of CaMKIIα catalytic domain pairing in living cells. Cells were transfected with DNA constructs encoding CaMKIIα tagged on the catalytic domain with either Cerulean or Venus. Cells transfected with Cerulean-CaMKIIα & free Venus monomers were used as a negative FRET control. Cells transfected with C5V was used as a positive FRET control. Each point is the average FRET efficiency and fraction donor value measured for an individual cell. Dashed lines are linear fits.</p