FCSlib (version 1.3.0)

fcs: Fluorescence Correlation Spectroscopy

Description

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

Usage

fcs(x , y = NULL, nPoints, pcf = FALSE)

Arguments

x

Numeric vector of length N.

y

Numeric vector of length N.

nPoints

The size of the sub-vectors in which the input vectors will be divided. This number must be less than N/2.

pcf

A boolean parameter to determine if an alternate version of the correlation function is used for the calculation of de pCF and pComb functions.

Value

A numeric vector G containing either the autocorrelation for the input vector x, or the cross-correlation between x and y vectors, with a length of nPoints.

Details

Fluorescence correlation spectroscopy (FCS) is a technique with high spatial and temporal resolution used to analyze the kinetics of particles diffusing at low concentrations. The detected fluorescence intensity as a function of time is: F(t).

The correlation function is computed as the normalized autocorrelation function, G(tau) = <deltaF(t)deltaF(t+tau)>/(<F(t)>*<F(t)>), to the collected data set, where t refers to a time point of flourescence acquisition, and tau refers to the temporal delay between acquisitions and <...> indicates average.

The correlation between deltaF(t) = F(t) - <F(t)> and deltaF(t+tau) = F(t+tau) - <F(t)> is calculated for a range of delay times. For temporal acquisitions as FCS point, x takes the value of F(t) and y = NULL. For cross-correlation experiments between two fluorescent signals x = F1(t) and y = F2(t), as channels, the correlation function is: G(tau) = <deltaF1(t) deltaF2(t+tau)> / (<F1(t)> <F2(t)>).

The function separate the original vector in sub-vectors of same length (n-points), then calculate an autocorrelation function form each sub-vector. The final result will be an average of all the autocorrelation functions.

References

R.A. Migueles-Ramirez, A.G. Velasco-Felix, R. Pinto-C<U+00E1>mara, C.D. Wood, A. Guerrero. Fluorescence fluctuation spectroscopy in living cells. Microscopy and imaging science: practical approaches to applied research and education, 138-151,2017.

See Also

gcf

Examples

# NOT RUN {
### 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.
# Use readFileTiff() function to read the fcs data in TIFF format.

f<-readFileTiff("Cy5_100nM.tif")

### Note that $f$ is a matrix of 2048 x 5000 x 1 dimentions.
# This is due to the fact that this single-point FCS experimen twas collected
# at intervals of 2048 points each, with an acquisition time of 2 mu s.
# Let's now create a dataframe with the FCS data wich here-and-after will be called Cy5.

acqTime = 2E-6
f<-as.vector(f)
time <- (1:length(f))*acqTime
Cy5<-data.frame(t = time, f)

### The first 100 ms of the time series are:

plot(Cy5[1:5000,], type ="l", xlab = "t(s)", ylab ="Fluorescence Intensity", main = "Cy5")

# The fcs() function receives three parameters: 'x' (mandatory),
# 'y'(optional) and 'nPoints' (optional), where x is the main signal to analyze,
#  y is a secondary signal (for the case of cross-correlation instead of autocorrelation)
# and nPoints is the final length of the calculated correlation curve.
# This function divides the original N-size signal into sub-vectors with a size of nPoints*2.
# Once all the sub-vectors are analyzed, these are then averaged.
# To use the fcs() function type

g <- fcs(x = Cy5$f, nPoints = length(Cy5$f)/2)

# The result of the function is assigned to the variable 'g',
# which contains the autocorrelation curve

length <- 1:length(g)
tau <-Cy5$t[length]
G<-data.frame(tau,g)
plot(G, log = "x", type = "l", xlab = expression(tau(s)), ylab = expression(G(tau)), main = "Cy5")

# It is important to remove the first point from the data,
# where G(\tau=0) it is not properly computed

G<-G[-1,]
plot(G, log = "x", type = "l", xlab = expression(tau(s)), ylab = expression(G(tau)), main = "Cy5")

# The variable 'nPoints' can be adjusted to better assess the transport phenomena
# in study (i.e. free diffusion in three dimensions in the case of this example) and
# for better understanding of the diffusive nature of the molecules.
# In this example 'nPoints' will be set to 2048.

g <- fcs(x = Cy5$f,nPoints = 2048)
length <- 1:length(g)
tau <-Cy5$t[length]
G<-data.frame(tau,g)
G<-G[-1,]
plot(G, log = "x", type = "l", xlab = expression(tau(s)), ylab = expression(G(tau)), main = "Cy5")
# }