Abstract
Förster resonance energy transfer (FRET) describes a physical phenomenon widely applied in biomedical research to estimate separations between biological molecules. Routinely, genetic engineering is used to incorporate spectral variants of the green fluorescent protein (GFPs), into cellular expressed proteins. The transfer efficiency or rate of energy transfer between donor and acceptor FPs is then assayed. As appreciable FRET occurs only when donors and acceptors are in close proximity (1-10nm), the presence of FRET may indicate that the engineered proteins associate as interacting species. For a homogeneous population of FRET pairs the separations between FRET donors and acceptors can be estimated from a measured FRET efficiency if it is assumed that donors and acceptors are randomly oriented and rotate extensively during their excited state (dynamic regime). Unlike typical organic fluorophores, the rotational correlation-times of FPs are typically much longer than their fluorescence lifetime; accordingly FPs are virtually static during their excited state. Thus, estimating separations between FP FRET pairs is problematic. To overcome this obstacle, we present here a simple method for estimating separations between FPs using the experimentally measured average FRET efficiency. This approach assumes that donor and acceptor fluorophores are randomly oriented, but do not rotate during their excited state (static regime). This approach utilizes a Monte-Carlo simulation generated look-up table that allows one to estimate the separation, normalized to the Förster distance, from the average FRET efficiency. Assuming a dynamic regime overestimates the separation significantly (by 10% near 0.5 and 30% near 0.75 efficiencies) compared to assuming a static regime, which is more appropriate for estimates of separations between FPs.
🔬 Techniques
✨ Fluorophores
💻 Software Details
🏛️ Research Organizations (ROR)
Affiliated research institutions:
📋 Methods
2.1. Monte Carlo simulations Monte Carlo simulations were performed in Igor Pro (ver6.22) to generate populations of FRET efficiencies in the static random isotropic orientational regime. Each simulation was based on generating 1,000,000 random replicate E values for a given Φ value. Two hundred and fifty Φ values were generated between a starting value of 0.01 and a final value of 2.5 in 0.01 increments. For each replicate the following equation was used to calculate a single FRET efficiency: (9) E static = κ 2 · 3 2 · ( 1 Φ ) 6 κ 2 · 3 2 · ( 1 Φ ) 6 + 1 where κ 2 was stochastically generated for each replicate to simulate FRET in the isotropic static regime. A distribution of 1,000,000 κ 2 values was generated from random values for the angles θ and ω , generated as previously described [ 18 ]. In brief, a uniform distribution of numbers ranging from 0 to 1 was generated using the Igor Pro enoise command. Next, the inverse cosine of these values was calculated to generate a population of angles expected for an isotropic distribution. These values of θ and ω were used in Eq. (5) to generate the population of κ 2 values, and these in turn were used in Eq. (9) to calculate FRET efficiencies in the static regime. The average FRET efficiency, 〈 E 〉, standard deviation, SD, skewness, and kurtosis of Monte Carlo simulation generated FRET efficiency populations were calculated using the Igor Pro wavestats command, using the following equations: (10) 〈 E 〉 = ∑ i = 0 i = 999,999 E i 1,000,000 (11) S D = 1 999,999 ∑ ( E − 〈 E 〉 ) 2 (12) Skewness = 1 1,000,000 ∑ i = 0 i = 999,999 [ E − 〈 E 〉 S D ] 3 (13) Kurtosis = 1 1,000,000 ∑ i = 0 i = 999,999 [ E − 〈 E 〉 S D ] 4 − 3
📊 Figures
Fig. 1
Isotropic u03ba 2 distribution. (A) Cartoon illustrating how the dipole orientation factor u03ba 2 is determined by 2 angles, u03b8 and u03c9 (see Eq. (5) ). Blue arrow depicts the position and orient...
Fig. 2
Monte Carlo simulations used to determine the relationship between average FRET efficiency and Separation under static isotropic conditions. The probability distribution of FRET efficiencies derived f...
Fig. 3
Moment Analysis of the dependence of FRET efficiency on Separation under static isotropic conditions. A. The dependence of u3008 E u3009 (the first moment of these populations) on u03a6 under isotropi...
Fig. 4
The dependence of Separation on average FRET efficiency under static isotropic conditions. The dependence of u03a6 on u3008 E u3009 under isotropic static (Blue) conditions. Dashed RED line depicts a ...
Figure images are served from the NIH/NLM PubMed Central Open Access Subset or Europe PMC; copyright remains with the publishers and authors.
💬 Discussion
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