kp: Calculates kinetic parameters as a function of model fit for...

In OenoKPM: Modeling the Kinetics of Carbon Dioxide Production in Alcoholic Fermentation

Calculates kinetic parameters as a function of model fit for CO₂ production as a function of time

Description

A function that, based on the observed data, the independent variable (e.g. time in h) and the dependent variable (e.g. CO₂ production in g L^-1), performs the modeling of the fermentation curve based on the chosen model (5PL, Gompertz, or 4PL).

Next, the coefficients are used in mathematical formulas to obtain the following kinetic parameters:

t_Lag - Duration of the latency phase for CO₂ production;

V_max - Maximum rate of production of CO₂;

t_Vmax - Moment in which maximum fermentation rate occurs;

CO_2Vmax - CO₂ Produced until Maximum fermentation rate occurs;

Y_max - Maximum production of carbon dioxide (CO₂);

Usage

kp(
  data,
  model,
  save.xls = FALSE,
  dir.save,
  xls.name,
  startA,
  startB,
  startC,
  startD,
  startG
)

Arguments

data	Data frame to be analyzed. The data frame must be in the following order: First: All columns containing the independent variable (e.g. time in hours) Second: All columns containing dependent variables (e.g. CO2 g L-1 production) Header: Columns must contain a header. If the treatment ID is in the header, this ID will be used to identify the coefficients and kinetic parameters for each analyzed curve.
model	Model to be adjusted. Argument for model: Model = 1. 5PL Model (five-parameter logistic (5PL) model). Model = 2. Gompertz Model. Model = 3. 4PL Model (four-parameter logistic (4PL) model).
save.xls	If TRUE, an xlsx file containing the coefficients and kinetic parameters will be saved in the working directory. If FALSE, the xlsx file will not be saved.
dir.save	Directory path where the xlsx file is to be saved.
xls.name	File name. Must contain the format. For example, "Parameters.xlsx".
startA	Starting estimate of the value of A for model.
startB	Starting estimate of the value of B for model.
startC	Starting estimate of the value of C for model.
startD	Starting estimate of the value of D for model.
startG	Starting estimate of the value of G for model.

Details

Curve fitting from the observed data is performed by the nlsLM() function in the 'minpack.lm' package.

You can see our article for more details on the mathematical formulas used to obtain each kinetic parameter (Gava et al., 2020). In addition, feel free to use it as a reference in your works.

Value

The analyzed model coefficients and the calculated kinetic parameters are returned in a data.frame. In addition, a "Parameters.xlsx" file can be generated, containing the coefficients and kinetic parameters of each studied fermentation curve.

Author(s)

Angelo Gava

References

Gava, A., Borsato, D., & Ficagna, E. (2020). Effect of mixture of fining agents on the fermentation kinetics of base wine for sparkling wine production: Use of methodology for modeling. LWT, 131, 109660. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1016/j.lwt.2020.109660")}

Zwietering, M. H., Jongenburger, I., Rombouts, F. M., & Van't Riet, K. J. A. E. M. (1990). Modeling of the bacterial growth curve. Applied and environmental microbiology, 56(6), 1875-1881. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1128/aem.56.6.1875-1881.1990")}

Examples

#Creating a data.frame. 
#First, columns containing independent variable.
#Second, columns containing dependent variable.
#The data frame created presents two 
#fermentation curves for two yeasts with 
#different times and carbon dioxide production.

df <- data.frame('Time_Yeast_A' = seq(0,280, by=6.23),
                 'Time_Yeast_B' = seq(0,170, by=3.7777778),
                 'CO2_Production_Yeast_A' = c(0,0.97,4.04,9.62,13.44,17.50,
                                              24.03,27.46,33.75,36.40,40.80,
                                             44.24,48.01,50.85,54.85,57.51,
                                             61.73,65.43,66.50,72.41,75.47,
                                             77.22,78.49,79.26,80.31,81.04,
                                             81.89,82.28,82.56,83.13,83.62,
                                             84.11,84.47,85.02,85.31,85.61,
                                             86.05,86.27,85.29,86.81,86.94,
                                             87.13,87.33,87.45,87.85),
                 'CO2_Production_Yeast_B' = c(0,0.41,0.70,3.05,15.61,18.41,
                                              21.37,23.23,28.28,41.28,43.98,
                                              49.54,54.43,60.40,63.75,69.29,
                                              76.54,78.38,80.91,83.72,84.66,
                                              85.39,85.81,86.92,87.38,87.61,
                                              88.38,88.57,88.72,88.82,89.22,
                                              89.32,89.52,89.71,89.92,90.11,
                                              90.31,90.50,90.70,90.90,91.09,
                                              91.29,91.49,91.68,91.88))

#Using the kp() function to find the 
#coefficients and kinetic parameters 
#according to the adopted model.

kp(data = df,
model = 1, 
startA = 0,
startB = 1.5,
startC = 500,
startD = 92, 
startG = 1500,
save.xls = FALSE) #5PL Model adopted

kp(data = df,model = 2,
startA = 92,
startB = 1.5,
startC = 0,
startD = NA, 
startG = NA, 
save.xls = FALSE) #Gompertz Model adopted

kp(data = df,
startA = 0,
startB = 2.5,
startC = 10,
startD = 92, 
startG = NA,
model = 3, 
save.xls = FALSE) #4PL Model adopted

#Saving an xlsx file. In this example, 
#we will use saving a temporary file in 
#the temporary file directories.

OenoKPM documentation built on May 29, 2024, 9:13 a.m.