flFitSpline: Perform a smooth spline fit on fluorescence data

In QurvE: Robust and User-Friendly Analysis of Growth and Fluorescence Curves

Perform a smooth spline fit on fluorescence data

Description

flFitSpline performs a smooth spline fit on the dataset and determines the greatest slope as the global maximum in the first derivative of the spline.

Usage

flFitSpline(
  time = NULL,
  growth = NULL,
  fl_data,
  ID = "undefined",
  control = fl.control(biphasic = FALSE, x_type = c("growth", "time"), log.x.spline =
    FALSE, log.y.spline = FALSE, smooth.fl = 0.75, t0 = 0, min.growth = NA)
)

Arguments

time	Vector of the independent variable: time (if x_type = 'time' in fl.control object.
growth	Vector of the independent variable: growth (if x_type = 'growth' in fl.control object.
fl_data	Vector of dependent variable: fluorescence.
ID	(Character) The name of the analyzed sample.
control	A fl.control object created with fl.control, defining relevant fitting options.
biphasic	(Logical) Shall flFitLinear and flFitSpline try to extract fluorescence parameters for two different phases (as observed with, e.g., regulator-promoter systems with varying response in different growth stages) (TRUE) or not (FALSE)?
x_type	(Character) Which data type shall be used as independent variable? Options are 'growth' and 'time'.
log.x.spline	(Logical) Indicates whether ln(x+1) should be applied to the independent variable for spline fits. Default: FALSE.
log.y.spline	(Logical) Indicates whether ln(y/y0) should be applied to the fluorescence data for spline fits. Default: FALSE
smooth.fl	(Numeric) Parameter describing the smoothness of the spline fit; usually (not necessary) within (0;1]. smooth.gc=NULL causes the program to query an optimal value via cross validation techniques. Especially for datasets with few data points the option NULL might cause a too small smoothing parameter. This can result a too tight fit that is susceptible to measurement errors (thus overestimating slopes) or produce an error in smooth.spline or lead to overfitting. The usage of a fixed value is recommended for reproducible results across samples. See smooth.spline for further details. Default: 0.55
t0	(Numeric) Minimum time value considered for linear and spline fits.
min.growth	(Numeric) Indicate whether only values above a certain threshold should be considered for linear regressions or spline fits.

Details

If biphasic = TRUE, the following steps are performed to define a second phase:

1. Determine local minima within the first derivative of the smooth spline fit.

2. Remove the 'peak' containing the highest value of the first derivative (i.e., mu_{max}) that is flanked by two local minima.

3. Repeat the smooth spline fit and identification of maximum slope for later time values than the local minimum after mu_{max}.

4. Repeat the smooth spline fit and identification of maximum slope for earlier time values than the local minimum before mu_{max}.

5. Choose the greater of the two independently determined slopes as mu_{max}2.

Value

A flFitSpline object. The lag time is estimated as the intersection between the tangent at the maximum slope and the horizontal line with y = y_0, where y0 is the first value of the dependent variable. Use plot.flFitSpline to visualize the spline fit and derivative over time.

x.in	Raw x values provided to the function as time or growth.
fl.in	Raw fluorescence data provided to the function as fl_data.
raw.x	Filtered x values used for the spline fit.
raw.fl	Filtered fluorescence values used for the spline fit.
ID	(Character) Identifies the tested sample.
fit.x	Fitted x values.
fit.fl	Fitted fluorescence values.
parameters	List of determined parameters.

• A: Maximum fluorescence.

• dY: Difference in maximum fluorescence and minimum fluorescence.

• max_slope: Maximum slope of fluorescence-vs.-x data (i.e., maximum in first derivative of the spline).

• x.max: Time at the maximum slope.

• lambda: Lag time.

• b.tangent: Intersection of the tangent at the maximum slope with the abscissa.

• max_slope2: For biphasic course of fluorescence: Maximum slope of fluorescence-vs.-x data of the second phase.

• lambda2: For biphasic course of fluorescence: Lag time determined for the second phase.

• x.max2: For biphasic course of fluorescence: Time at the maximum slope of the second phase.

• b.tangent2: For biphasic course of fluorescence: Intersection of the tangent at the maximum slope of the second phase with the abscissa.

• integral: Area under the curve of the spline fit.

spline	smooth.spline object generated by the smooth.spline function.
spline.deriv1	list of time ('x') and growth ('y') values describing the first derivative of the spline fit.
reliable	(Logical) Indicates whether the performed fit is reliable (to be set manually).
fitFlag	(Logical) Indicates whether a spline fit was successfully performed on the data.
fitFlag2	(Logical) Indicates whether a second phase was identified.
control	Object of class fl.control containing list of options passed to the function as control.

See Also

Other fluorescence fitting functions: flBootSpline(), flFit()

Examples

# load example dataset
input <- read_data(data.growth = system.file("lac_promoters_growth.txt", package = "QurvE"),
                   data.fl = system.file("lac_promoters_fluorescence.txt", package = "QurvE"),
                   csvsep = "\t",
                   csvsep.fl = "\t")

# Extract time and normalized fluorescence data for single sample
time <- input$time[4,]
data <- input$norm.fluorescence[4,-(1:3)] # Remove identifier columns

# Perform linear fit
TestFit <- flFitSpline(time = time,
                       fl_data = data,
                       ID = 'TestFit',
                       control = fl.control(fit.opt = 's', x_type = 'time'))

plot(TestFit)

QurvE documentation built on May 29, 2024, 3 a.m.