Updated 2017 November 22nd
Many biological phenomena follow four different types of relationships that include sigmoid, exponential, linear and Michaelis-Menten (MM) type relationships. The MM model is given by
where is the reaction rate of product to substrate , represents the maximum rate achieved by the system, and is the substrate concentration at which the reaction rate is half of . This is a short post on fitting a Michaelis-Menten curve to data using the drc package for R available in CRAN. To get started install and load the drc package.
#install if necessary install.packages("drc") library(drc)
I’ll use the same data as this blog post.
# substrate S <- c(0,1,2,5,8,12,30,50) # reaction rate v <- c(0,11.1,25.4,44.8,54.5,58.2,72.0,60.1) kinData <- data.frame(S,v) # use the two parameter MM model (MM.2) m1 <- drm(v ~ S, data = kinData, fct = MM.2()) # the summary indicates how well the curve fits the data summary(m1) Model fitted: Michaelis-Menten (2 parms) Parameter estimates: Estimate Std. Error t-value p-value d:(Intercept) 73.26127 4.36676 16.7770 2.864e-06 *** e:(Intercept) 3.43714 0.75484 4.5535 0.003878 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 5.106323 (6 degrees of freedom) plot(m1, log = '', pch = 17, main = "Fitted MM curve")
To get and use coef() in R to get the coefficients of the model.
coef(m1) d:(Intercept) e:(Intercept) 73.261268 3.437136
My post on curve fitting in R
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