fitFCS: Fitting FCS Data
In FCSlib: A Collection of Fluorescence Fluctuation Spectroscopy Analysis Methods

Description Usage Arguments Details Value Author(s) See Also Examples

Estimates the parameters based on a given equation, on the data generated with the fcs() function.

1 2	fitFCS(data = parent.frame(), start, low = -Inf, up = Inf, type = "D3D", model = NULL, trace = TRUE)

`data`	data frame in which to evaluate the variables in formula and weights.
`start`	a named list or named numeric vector of starting estimates.
`low, up`	a named list or named numeric vector of lower and upper bounds, replicated to be as long as start. If unspecified, all parameters are assumed to be -Inf and Inf.
`type`	specification for the equation to model, is a character string. The default value is "D3D" equation for three-dimensional free diffusion. Another possibles values are: "D2D" for two-dimensional free diffusion, "D2DT" for two-dimensional free diffusion with triplet exited state, and "D3DT" for three-dimensional free diffusion with triplet exited state and D3D2S for two species in three-dimensional free diffusion.
`model`	a character type variable, that must contain the custom equation if needed, NULL by default.
`trace`	logical value that indicates whether the progress of the non-linear regression (nls) should be printed.

A transport model, containing physical information about the diffusive nature of the fluorophores, can be fitted to the autocorrelation data to obtain parameters such as the diffusion coeficient D and the number of molecules within the observation volume N.

The fitFCS() function uses the 'Non-linear Least Squares' function to fit a physical model into a data set. There are four possible models to be fit:

"D2D" for two-dimensional diffusion

"D2DT" for two-dimensional diffusion with triplet state

"D3D" for three-dimensional diffusion

"D3DT" for three-dimensional diffusion with triplet state

Inside the equations for each model, gamma a geometric factor that depends on the illumination profile. For confocal excitation its magnitude approaches gamma = 1/sqrt8 ??? 0.35 fl. The diffusion time is defined as tau_D = s^2/4D, where s and u are the radius and the half-length of the focal volume, respectively. The parameter u is usually expressed as u = ks, with k being the eccentricity of the focal volume; for confocal excitation k ??? 3. The fraction of molecules in the triplet state is B, and tau_B is a time constant for the triplet state.

A nls object (from nls).

Raúl Pinto Cámara.

nls, fcs

# Load the FCSlib package

library(FCSlib)

g <- fcs(x = Cy5$f,nPoints = 2048)
len <- 1:length(g)
tau <-Cy5_100nM$t[len]
G<-data.frame(tau,g)
G<-G[-1,]

# Once the correlation curve 'g' has been generated,
# a data frame containing known parameters must be then defined

df<-data.frame(G, s = 0.27, k = 3)
head(df)

# The radius of the focal volume must computed experimentally.
# For this example, we choose a s = 0.27~ mu m
# Then, three lists that contain the initial values of the data,
# as well as the upper and lower limits of these values, must be defined.
# The input values here are the expected values for the real experimental data
# to be very similar or close to, so that the function calculates them accurately.
# Initial values:

start <- list(D = 100, G0 = 0.1)
up <- list(D = 1E3, G0 = 10)
low <- list(D = 1E-1, G0 = 1E-2)

# Once the known parameters are defined, we now proceed to use the fitFCS() function.
# The result will be a nls object

modelFCS <- fitFCS(df, start, low, up, type = "D3D", trace = F)
# summary(modelFCS)

# By using the predict() function, the object generated in the previous step
# is transformed into a vector that contains the curve fitted by the desired model.

fit <- predict(modelFCS, tau)

# Finally, use the following command to obtain the resulting graph,
# where the blue line corresponds to the fitted data and the black surface
# corresponds to the unfitted

plot (G, log = "x", type = "l", xlab = expression(tau(s)),
      ylab = expression(G(tau)), main = "Cy5")
lines(fit~G$tau, col = "blue")

# To acquire access to the physical coefficients of the model type

s<-summary(modelFCS)
s$coefficients[,1]