gcf {FCSlib}

General Correlation Function

Description

Performs either the auto-correlation or cross-correlation between vectors x and y, returning a correlation function.

Usage

gcf(x, y, xmean = 1, ymean = 1, c = 0)

Arguments

x

A numerical signal with dimensions M x N x Z.

y

A numerical signal with dimensions M x N x Z.

xmean

The mean value of the signal x.

ymean

The mean value of the signal y.

c

A numeric variable to restrict the correlation to positives values.

Details

The number of emission events per unit time is determined and used to generate autocorrelation and cross-correlation curves from the intensity traces F(t) and the fluctuations deltaF(t) = F(t)-<F(t)>. The auto-correlation function of the collected data set, is computed as the normalized auto-correlation function, when y=x. The general auto-correlation function is defined as: G(tau) = (deltaF(t) deltaF(t+tau) )/(<F(t)> <F(t)>), where t refers to a time point of fluorescence acquisition, and tau refers to the temporal delay between acquisitions. <...> is the temporal average of F(t); and deltaF(t) = F(t)-<F(t)>, deltaF(t+tau) = F(t+tau)-<F(t)>.

For temporal acquisitions such as point FCS, x and y are F(t). The cross-correlation function between two channels of fluorescent signals, x = F1(t) and y = F2(t), the cross-correlation function is defined as: G(tau) = (deltaF1(t) deltaF2(t+tau) )/(<F1(t)><F2(t)>), where xmean = <F1(t)> and ymean = <F2(t)> are the mean values of the fluorescent signals.

Value

G A numerical signal with dimension N' x M' x Z'

Author(s)

Raúl Pinto Cámara.

References

Siegel, A. P., Hays, N. M., & Day, R. N. (2013). Unraveling transcription factor interactions with heterochromatin protein 1 using fluorescence lifetime imaging microscopy and fluorescence correlation spectroscopy. Journal of biomedical optics, 18(2), 025002.

See Also

fcs, convolve

Examples

# Load the FCSlib package

library(FCSlib)

# As an example, we will use data from experiment adquisition
# of free Cy5 molecules diffusing in water at a concentration of 100 nM.

oldpar <- par(no.readonly = TRUE)
g <- gcf(x = Cy5$f, y = Cy5$f, xmean = mean(Cy5$f), ymean = mean(Cy5$f))
length <- 1:length(g)
par(mfrow=c(1,1))
plot(y = g, x = Cy5$t[length], log = 'x', type = 'l',
xlab = expression(tau(mu~s)), ylab = expression(G(tau)),
main = "Cy5 100nM")
par(oldpar)