FRET Correction Formulas¶
The fretmath
module contains functions to compute corrected FRET efficiency
from the proximity ratio and viceversa.
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 crosssections at the donorexcitation 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 crosssections at the donorexcitation 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 crosssections at the donorexcitation 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 crosssection at donorexcitation 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()
.