FRET Correction Formulas¶
The fretmath
module contains functions to compute corrected FRET efficiency
from the proximity ratio and vice-versa.
For derivation see notebook: “Derivation of FRET and S correction formulas.ipynb” (link).
- fretbursts.fretmath.correct_E_gamma_leak_dir(Eraw, gamma=1, leakage=0, dir_ex_t=0)¶
Compute corrected FRET efficiency from proximity ratio
Eraw
.For the inverse function see
uncorrect_E_gamma_leak_dir()
.- Parameters
Eraw (float or array) – proximity ratio (only background correction, no gamma, leakage or direct excitation)
gamma (float) – gamma factor
leakage (float) – leakage coefficient
dir_ex_t (float) – coefficient expressing the direct excitation as n_dir = dir_ex_t * (na + gamma*nd). In terms of physical parameters it is the ratio of acceptor over donor absorption cross-sections at the donor-excitation wavelength.
- Returns
Corrected FRET effciency
- fretbursts.fretmath.correct_S(Eraw, Sraw, gamma, leakage, dir_ex_t)¶
Correct S values for gamma, leakage and direct excitation.
- Parameters
Eraw (scalar or array) – uncorrected (“raw”) E after only background correction (no gamma, leakage or direct excitation).
Sraw (scalar or array) – uncorrected (“raw”) S after only background correction (no gamma, leakage or direct excitation).
gamma (float) – gamma factor.
leakage (float) – donor emission leakage into the acceptor channel.
dir_ex_t (float) – direct acceptor excitation by donor laser. Defined as
n_dir = dir_ex_t * (na + g nd)
. The dir_ex_t coefficient is the ratio between D and A absorption cross-sections at the donor-excitation wavelength.
- Returns
Corrected S (stoichiometry), same size as
Sraw
.
- fretbursts.fretmath.dir_ex_correct_E(Eraw, dir_ex_t)¶
Apply direct excitation correction to the uncorrected FRET
Eraw
.The coefficient
dir_ex_t
expresses the direct excitation as n_dir = dir_ex_t * (na + gamma*nd). In terms of physical parameters it is the ratio of acceptor over donor absorption cross-sections at the donor-excitation wavelength.For the inverse see
dir_ex_uncorrect_E()
.
- fretbursts.fretmath.dir_ex_uncorrect_E(E, dir_ex_t)¶
Reverse direct excitation correction and return uncorrected FRET.
For the inverse see
dir_ex_correct_E()
.
- fretbursts.fretmath.gamma_correct_E(Eraw, gamma)¶
Apply gamma correction to the uncorrected FRET
Eraw
.For the inverse see
gamma_uncorrect_E()
.
- fretbursts.fretmath.gamma_uncorrect_E(E, gamma)¶
Reverse gamma correction and return uncorrected FRET.
For the inverse see
gamma_correct_E()
.
- fretbursts.fretmath.leakage_correct_E(Eraw, leakage)¶
Apply leakage correction to the uncorrected FRET
Eraw
.For the inverse see
leakage_uncorrect_E()
.
- fretbursts.fretmath.leakage_uncorrect_E(E, leakage)¶
Reverse leakage correction and return uncorrected FRET.
For the inverse see
leakage_correct_E()
.
- fretbursts.fretmath.test_fretmath()¶
Run a few consistency checks for the correction functions.
- fretbursts.fretmath.uncorrect_E_gamma_leak_dir(E, gamma=1, leakage=0, dir_ex_t=0)¶
Compute proximity ratio from corrected FRET efficiency
E
.This function is the inverse of
correct_E_gamma_leak_dir()
.- Parameters
E (float or array) – corrected FRET efficiency
gamma (float) – gamma factor
leakage (float) – leakage coefficient
dir_ex_t (float) – direct excitation coefficient expressed as n_dir = dir_ex_t * (na + gamma*nd). In terms of physical parameters it is the ratio of absorption cross-section at donor-excitation wavelengths of acceptor over donor.
- Returns
Proximity ratio (reverses gamma, leakage and direct excitation)
- fretbursts.fretmath.uncorrect_S(E_R, S, gamma, L_k, d_dirT)¶
Function used to test
correct_S()
.