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b/docs/articles/FOCUS_D.html index 0ce7bd07..ad53126e 100644 --- a/docs/articles/FOCUS_D.html +++ b/docs/articles/FOCUS_D.html @@ -16,14 +16,27 @@
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:03 2016 
-## Date of summary: Fri Nov 18 15:22:03 2016 
+## Date of fit:     Fri Nov 18 16:48:11 2016 
+## Date of summary: Fri Nov 18 16:48:11 2016 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.09 s
+## Fitted with method Port using 37 model solutions performed in 0.085 s
 ## 
 ## Weighting: none
 ## 
@@ -156,8 +169,8 @@ FOCUS_2006_L1_mkin <- 
summary(m.L1.FOMC, data = FALSE)
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:04 2016 
-## Date of summary: Fri Nov 18 15:22:04 2016 
+## Date of fit:     Fri Nov 18 16:48:12 2016 
+## Date of summary: Fri Nov 18 16:48:12 2016 
 ## 
 ## 
 ## Warning: Optimisation by method Port did not converge.
@@ -169,7 +182,7 @@ FOCUS_2006_L1_mkin <-  
summary(m.L2.FOMC, data = FALSE)
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:05 2016 
-## Date of summary: Fri Nov 18 15:22:05 2016 
+## Date of fit:     Fri Nov 18 16:48:13 2016 
+## Date of summary: Fri Nov 18 16:48:13 2016 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 81 model solutions performed in 0.19 s
+## Fitted with method Port using 81 model solutions performed in 0.196 s
 ## 
 ## Weighting: none
 ## 
@@ -323,8 +336,8 @@ FOCUS_2006_L2_mkin <- 
summary(m.L2.DFOP, data = FALSE)
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:06 2016 
-## Date of summary: Fri Nov 18 15:22:06 2016 
+## Date of fit:     Fri Nov 18 16:48:14 2016 
+## Date of summary: Fri Nov 18 16:48:14 2016 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -333,7 +346,7 @@ FOCUS_2006_L2_mkin <-  
summary(mm.L3[["DFOP", 1]])
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:07 2016 
-## Date of summary: Fri Nov 18 15:22:07 2016 
+## Date of fit:     Fri Nov 18 16:48:15 2016 
+## Date of summary: Fri Nov 18 16:48:15 2016 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -422,7 +435,7 @@ mm.L3 <-  
summary(mm.L4[["SFO", 1]], data = FALSE)
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:08 2016 
-## Date of summary: Fri Nov 18 15:22:08 2016 
+## Date of fit:     Fri Nov 18 16:48:15 2016 
+## Date of summary: Fri Nov 18 16:48:16 2016 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.109 s
+## Fitted with method Port using 46 model solutions performed in 0.107 s
 ## 
 ## Weighting: none
 ## 
@@ -572,8 +585,8 @@ mm.L4 <- 
summary(mm.L4[["FOMC", 1]], data = FALSE)
## mkin version:    0.9.44.9000 
 ## R version:       3.3.2 
-## Date of fit:     Fri Nov 18 15:22:08 2016 
-## Date of summary: Fri Nov 18 15:22:08 2016 
+## Date of fit:     Fri Nov 18 16:48:16 2016 
+## Date of summary: Fri Nov 18 16:48:16 2016 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
diff --git a/docs/articles/FOCUS_Z.aux b/docs/articles/FOCUS_Z.aux
deleted file mode 100644
index f997f2d7..00000000
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+++ /dev/null
@@ -1,26 +0,0 @@
-\relax 
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-\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
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-\citation{FOCUSkinetics2011}
-\@writefile{toc}{\contentsline {section}{\numberline {1}The data}{1}{section.1}}
-\@writefile{toc}{\contentsline {section}{\numberline {2}Parent compound and one metabolite}{2}{section.2}}
-\@writefile{toc}{\contentsline {section}{\numberline {3}Including metabolites Z2 and Z3}{8}{section.3}}
-\@writefile{toc}{\contentsline {section}{\numberline {4}Using the SFORB model for parent and metabolites}{12}{section.4}}
-\bibstyle{plainnat}
-\bibdata{references}
-\bibcite{FOCUSkinetics2011}{{1}{2011}{{FOCUS Work Group on Degradation Kinetics}}{{}}}
diff --git a/docs/articles/FOCUS_Z.bbl b/docs/articles/FOCUS_Z.bbl
deleted file mode 100644
index 451497c8..00000000
--- a/docs/articles/FOCUS_Z.bbl
+++ /dev/null
@@ -1,15 +0,0 @@
-\begin{thebibliography}{1}
-\providecommand{\natexlab}[1]{#1}
-\providecommand{\url}[1]{\texttt{#1}}
-\expandafter\ifx\csname urlstyle\endcsname\relax
-  \providecommand{\doi}[1]{doi: #1}\else
-  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi
-
-\bibitem[{FOCUS Work Group on Degradation Kinetics}(2011)]{FOCUSkinetics2011}
-{FOCUS Work Group on Degradation Kinetics}.
-\newblock \emph{Generic guidance for estimating persistence and degradation
-  kinetics from environmental fate studies on pesticides in EU registration},
-  1.0 edition, November 2011.
-\newblock URL \url{http://focus.jrc.ec.europa.eu/dk}.
-
-\end{thebibliography}
diff --git a/docs/articles/FOCUS_Z.blg b/docs/articles/FOCUS_Z.blg
deleted file mode 100644
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\ifdim\Gin@nat@width>\linewidth - \linewidth - \else - \Gin@nat@width - \fi -} -\makeatother - -\definecolor{fgcolor}{rgb}{0.345, 0.345, 0.345} -\newcommand{\hlnum}[1]{\textcolor[rgb]{0.686,0.059,0.569}{#1}}% -\newcommand{\hlstr}[1]{\textcolor[rgb]{0.192,0.494,0.8}{#1}}% -\newcommand{\hlcom}[1]{\textcolor[rgb]{0.678,0.584,0.686}{\textit{#1}}}% -\newcommand{\hlopt}[1]{\textcolor[rgb]{0,0,0}{#1}}% -\newcommand{\hlstd}[1]{\textcolor[rgb]{0.345,0.345,0.345}{#1}}% -\newcommand{\hlkwa}[1]{\textcolor[rgb]{0.161,0.373,0.58}{\textbf{#1}}}% -\newcommand{\hlkwb}[1]{\textcolor[rgb]{0.69,0.353,0.396}{#1}}% -\newcommand{\hlkwc}[1]{\textcolor[rgb]{0.333,0.667,0.333}{#1}}% -\newcommand{\hlkwd}[1]{\textcolor[rgb]{0.737,0.353,0.396}{\textbf{#1}}}% -\let\hlipl\hlkwb - -\usepackage{framed} -\makeatletter -\newenvironment{kframe}{% - \def\at@end@of@kframe{}% - \ifinner\ifhmode% - \def\at@end@of@kframe{\end{minipage}}% - \begin{minipage}{\columnwidth}% - \fi\fi% - \def\FrameCommand##1{\hskip\@totalleftmargin \hskip-\fboxsep - \colorbox{shadecolor}{##1}\hskip-\fboxsep - % There is no \\@totalrightmargin, so: - \hskip-\linewidth \hskip-\@totalleftmargin \hskip\columnwidth}% - \MakeFramed {\advance\hsize-\width - \@totalleftmargin\z@ \linewidth\hsize - \@setminipage}}% - {\par\unskip\endMakeFramed% - \at@end@of@kframe} -\makeatother - -\definecolor{shadecolor}{rgb}{.97, .97, .97} -\definecolor{messagecolor}{rgb}{0, 0, 0} -\definecolor{warningcolor}{rgb}{1, 0, 1} -\definecolor{errorcolor}{rgb}{1, 0, 0} -\newenvironment{knitrout}{}{} % an empty environment to be redefined in TeX - -\usepackage{alltt} -\usepackage{a4wide} -\input{header} -\hypersetup{ - pdftitle = {Example evaluation of FOCUS dataset Z}, - pdfsubject = {Manuscript}, - pdfauthor = {Johannes Ranke}, - colorlinks = {true}, - linkcolor = {blue}, - citecolor = {blue}, - urlcolor = {red}, - hyperindex = {true}, - linktocpage = {true}, -} -\IfFileExists{upquote.sty}{\usepackage{upquote}}{} -\begin{document} - - - -\title{Example evaluation of FOCUS dataset Z} -\author{\textbf{Johannes Ranke} \\[0.5cm] -%EndAName -Wissenschaftlicher Berater\\ -Kronacher Str. 8, 79639 Grenzach-Wyhlen, Germany\\[0.5cm] -and\\[0.5cm] -University of Bremen\\ -} -\maketitle - -\thispagestyle{empty} \setcounter{page}{0} - -\clearpage - -\tableofcontents - -\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation - -\section{The data} - -The following code defines the example dataset from Appendix 7 to the FOCUS kinetics -report \citep{FOCUSkinetics2011}, p.350. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{require}\hlstd{(mkin)} -\end{alltt} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: mkin}} - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: minpack.lm}} - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: rootSolve}} - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: inline}} - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: methods}} - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Loading required package: parallel}}\begin{alltt} -\hlstd{LOD} \hlkwb{=} \hlnum{0.5} -\hlstd{FOCUS_2006_Z} \hlkwb{=} \hlkwd{data.frame}\hlstd{(} - \hlkwc{t} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{0.04}\hlstd{,} \hlnum{0.125}\hlstd{,} \hlnum{0.29}\hlstd{,} \hlnum{0.54}\hlstd{,} \hlnum{1}\hlstd{,} \hlnum{2}\hlstd{,} \hlnum{3}\hlstd{,} \hlnum{4}\hlstd{,} \hlnum{7}\hlstd{,} \hlnum{10}\hlstd{,} \hlnum{14}\hlstd{,} \hlnum{21}\hlstd{,} - \hlnum{42}\hlstd{,} \hlnum{61}\hlstd{,} \hlnum{96}\hlstd{,} \hlnum{124}\hlstd{),} - \hlkwc{Z0} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{100}\hlstd{,} \hlnum{81.7}\hlstd{,} \hlnum{70.4}\hlstd{,} \hlnum{51.1}\hlstd{,} \hlnum{41.2}\hlstd{,} \hlnum{6.6}\hlstd{,} \hlnum{4.6}\hlstd{,} \hlnum{3.9}\hlstd{,} \hlnum{4.6}\hlstd{,} \hlnum{4.3}\hlstd{,} \hlnum{6.8}\hlstd{,} - \hlnum{2.9}\hlstd{,} \hlnum{3.5}\hlstd{,} \hlnum{5.3}\hlstd{,} \hlnum{4.4}\hlstd{,} \hlnum{1.2}\hlstd{,} \hlnum{0.7}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{18.3}\hlstd{,} \hlnum{29.6}\hlstd{,} \hlnum{46.3}\hlstd{,} \hlnum{55.1}\hlstd{,} \hlnum{65.7}\hlstd{,} \hlnum{39.1}\hlstd{,} \hlnum{36}\hlstd{,} \hlnum{15.3}\hlstd{,} \hlnum{5.6}\hlstd{,} \hlnum{1.1}\hlstd{,} - \hlnum{1.6}\hlstd{,} \hlnum{0.6}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{2.6}\hlstd{,} \hlnum{3.8}\hlstd{,} \hlnum{15.3}\hlstd{,} \hlnum{37.2}\hlstd{,} \hlnum{31.7}\hlstd{,} \hlnum{35.6}\hlstd{,} \hlnum{14.5}\hlstd{,} - \hlnum{0.8}\hlstd{,} \hlnum{2.1}\hlstd{,} \hlnum{1.9}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{),} - \hlkwc{Z3} \hlstd{=} \hlkwd{c}\hlstd{(}\hlnum{0}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{NA}\hlstd{,} \hlnum{0.5} \hlopt{*} \hlstd{LOD,} \hlnum{9.2}\hlstd{,} \hlnum{13.1}\hlstd{,} \hlnum{22.3}\hlstd{,} \hlnum{28.4}\hlstd{,} \hlnum{32.5}\hlstd{,} - \hlnum{25.2}\hlstd{,} \hlnum{17.2}\hlstd{,} \hlnum{4.8}\hlstd{,} \hlnum{4.5}\hlstd{,} \hlnum{2.8}\hlstd{,} \hlnum{4.4}\hlstd{))} - -\hlstd{FOCUS_2006_Z_mkin} \hlkwb{<-} \hlkwd{mkin_wide_to_long}\hlstd{(FOCUS_2006_Z)} -\end{alltt} -\end{kframe} -\end{knitrout} - -\section{Parent compound and one metabolite} - -The next step is to set up the models used for the kinetic analysis. As the -simultaneous fit of parent and the first metabolite is usually straightforward, -Step 1 (SFO for parent only) is skipped here. We start with the model 2a, -with formation and decline of metabolite Z1 and the pathway from parent -directly to sink included (default in mkin). - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.2a} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{))} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.2a} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.2a, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.2a)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_1-1} -\begin{kframe}\begin{alltt} -\hlkwd{summary}\hlstd{(m.Z.2a,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar} -\end{alltt} -\begin{verbatim} -## Estimate se_notrans t value Pr(>t) -## Z0_0 9.701488e+01 3.55313691 2.730401e+01 1.679214e-21 -## k_Z0_sink 1.281376e-11 0.22689470 5.647447e-11 5.000000e-01 -## k_Z0_Z1 2.236006e+00 0.16507604 1.354531e+01 7.396594e-14 -## k_Z1_sink 4.821248e-01 0.06585369 7.321150e+00 3.552015e-08 -## Lower Upper -## Z0_0 91.4058170 102.6239462 -## k_Z0_sink 0.0000000 Inf -## k_Z0_Z1 1.8419826 2.7143172 -## k_Z1_sink 0.4005856 0.5802613 -\end{verbatim} -\end{kframe} -\end{knitrout} - -As obvious from the parameter summary (the \texttt{bpar} component of the -summary), the kinetic rate constant from parent compound Z to sink -is negligible. Accordingly, the exact magnitude of the fitted parameter -\texttt{log k\_Z0\_sink} is ill-defined and the covariance matrix is not -returned (not shown, would be visible in the complete summary). -This suggests, in agreement with the analysis in the FOCUS kinetics report, to -simplify the model by removing the pathway to sink. - -A similar result can be obtained when formation fractions are used in the model -formulation: - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.2a.ff} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),} - \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.2a.ff} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.2a.ff, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.2a.ff)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_2-1} -\begin{kframe}\begin{alltt} -\hlkwd{summary}\hlstd{(m.Z.2a.ff,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar} -\end{alltt} -\begin{verbatim} -## Estimate se_notrans t value Pr(>t) Lower -## Z0_0 97.0148812 3.55314944 27.303912 1.679369e-21 91.3287912 -## k_Z0 2.2360064 0.21684747 10.311425 3.661846e-11 1.8052909 -## k_Z1 0.4821248 0.06585372 7.321147 3.552045e-08 0.3996826 -## f_Z0_to_Z1 1.0000000 0.10147342 9.854798 9.707056e-11 0.0000000 -## Upper -## Z0_0 102.7009713 -## k_Z0 2.7694843 -## k_Z1 0.5815722 -## f_Z0_to_Z1 1.0000000 -\end{verbatim} -\end{kframe} -\end{knitrout} - -Here, the ilr transformed formation fraction fitted in the model takes a very -large value, and the backtransformed formation fraction from parent Z to Z1 is -practically unity. Again, the covariance matrix is not returned as the model is -overparameterised. - -The simplified model is obtained by setting the list component \texttt{sink} to -\texttt{FALSE}.\footnote{If the model formulation without formation fractions -is used, the same effect can be obtained by fixing the parameter \texttt{k\_Z\_sink} -to a value of zero.} - -In the following, we use the parameterisation with formation fractions in order -to be able to compare with the results in the FOCUS guidance, and as it -makes it easier to use parameters obtained in a previous fit when adding a further -metabolite. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.3} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),} \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.3} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.3, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.3)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_3-1} -\begin{kframe}\begin{alltt} -\hlkwd{summary}\hlstd{(m.Z.3,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar} -\end{alltt} -\begin{verbatim} -## Estimate se_notrans t value Pr(>t) Lower -## Z0_0 97.0148815 2.68177093 36.17568 2.363587e-25 91.5215237 -## k_Z0 2.2360064 0.14686110 15.22531 2.246514e-15 1.9545310 -## k_Z1 0.4821248 0.04268712 11.29439 3.068581e-12 0.4021552 -## Upper -## Z0_0 102.5082392 -## k_Z0 2.5580177 -## k_Z1 0.5779966 -\end{verbatim} -\end{kframe} -\end{knitrout} - -As there is only one transformation product for Z0 and no pathway -to sink, the formation fraction is internally fixed to unity. - -\section{Including metabolites Z2 and Z3} - -As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as -well in the next step. While this step appears questionable on the basis of the above results, it -is followed here for the purpose of comparison. Also, in the FOCUS report, it is -assumed that there is additional empirical evidence that Z1 quickly and exclusively -hydrolyses to Z2. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.5} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),} \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.5} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.5, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.5)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_5-1} - -\end{knitrout} - -Finally, metabolite Z3 is added to the model. We use the optimised -differential equation parameter values from the previous fit in order to -accelerate the optimization. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.FOCUS} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),} - \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{),} - \hlkwc{use_of_ff} \hlstd{=} \hlstr{"max"}\hlstd{)} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.FOCUS} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.FOCUS, FOCUS_2006_Z_mkin,} - \hlkwc{parms.ini} \hlstd{= m.Z.5}\hlopt{$}\hlstd{bparms.ode,} - \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.FOCUS)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_6-1} -\begin{kframe}\begin{alltt} -\hlkwd{summary}\hlstd{(m.Z.FOCUS,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{bpar} -\end{alltt} -\begin{verbatim} -## Estimate se_notrans t value Pr(>t) Lower -## Z0_0 96.83849566 2.05886133 47.034977 5.583742e-44 92.70517559 -## k_Z0 2.21540897 0.11813046 18.753919 7.744034e-25 1.99051134 -## k_Z1 0.47829896 0.02928763 16.331089 3.333376e-22 0.42297603 -## k_Z2 0.45161653 0.04421268 10.214638 3.110936e-14 0.37103495 -## k_Z3 0.05869343 0.01429485 4.105914 7.285393e-05 0.03599566 -## f_Z2_to_Z3 0.47150952 0.05705233 8.264510 2.809889e-11 0.36038193 -## Upper -## Z0_0 100.97181573 -## k_Z0 2.46571661 -## k_Z1 0.54085782 -## k_Z2 0.54969886 -## k_Z3 0.09570371 -## f_Z2_to_Z3 0.58553462 -\end{verbatim} -\begin{alltt} -\hlkwd{endpoints}\hlstd{(m.Z.FOCUS)} -\end{alltt} -\begin{verbatim} -## $ff -## Z2_Z3 Z2_sink -## 0.4715095 0.5284905 -## -## $SFORB -## logical(0) -## -## $distimes -## DT50 DT90 -## Z0 0.3128755 1.039350 -## Z1 1.4491923 4.814113 -## Z2 1.5348136 5.098540 -## Z3 11.8096217 39.230714 -\end{verbatim} -\end{kframe} -\end{knitrout} - -This fit corresponds to the final result chosen in Appendix 7 of the FOCUS -report. Confidence intervals returned by mkin are based on internally -transformed parameters, however. - -\section{Using the SFORB model for parent and metabolites} - -As the FOCUS report states, there is a certain tailing of the time course of metabolite -Z3. Also, the time course of the parent compound is not fitted very well using the -SFO model, as residues at a certain low level remain. - -Therefore, an additional model is offered here, using the single first-order -reversible binding (SFORB) model for metabolite Z3. As expected, the $\chi^2$ -error level is lower for metabolite Z3 using this model and the graphical -fit for Z3 is improved. However, the covariance matrix is not returned. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.mkin.1} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),} - \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{))} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.mkin.1} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.1, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.mkin.1)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_7-1} -\begin{kframe}\begin{alltt} -\hlkwd{summary}\hlstd{(m.Z.mkin.1,} \hlkwc{data} \hlstd{=} \hlnum{FALSE}\hlstd{)}\hlopt{$}\hlstd{cov.unscaled} -\end{alltt} -\begin{verbatim} -## NULL -\end{verbatim} -\end{kframe} -\end{knitrout} - -Therefore, a further stepwise model building is performed starting from the -stage of parent and two metabolites, starting from the assumption that the model -fit for the parent compound can be improved by using the SFORB model. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.mkin.3} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{))} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.mkin.3} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.3, FOCUS_2006_Z_mkin,} \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.mkin.3)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_9-1} - -\end{knitrout} - -This results in a much better representation of the behaviour of the parent -compound Z0. - -Finally, Z3 is added as well. These models appear overparameterised (no -covariance matrix returned) if the sink for Z1 is left in the models. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.mkin.4} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),} - \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{))} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.mkin.4} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.4, FOCUS_2006_Z_mkin,} - \hlkwc{parms.ini} \hlstd{= m.Z.mkin.3}\hlopt{$}\hlstd{bparms.ode,} - \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.mkin.4)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_10-1} - -\end{knitrout} - -The error level of the fit, but especially of metabolite Z3, can be improved if -the SFORB model is chosen for this metabolite, as this model is capable of -representing the tailing of the metabolite decline phase. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{Z.mkin.5} \hlkwb{<-} \hlkwd{mkinmod}\hlstd{(}\hlkwc{Z0} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{,} \hlstr{"Z1"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z1} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z2"}\hlstd{,} \hlkwc{sink} \hlstd{=} \hlnum{FALSE}\hlstd{),} - \hlkwc{Z2} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFO"}\hlstd{,} \hlstr{"Z3"}\hlstd{),} - \hlkwc{Z3} \hlstd{=} \hlkwd{mkinsub}\hlstd{(}\hlstr{"SFORB"}\hlstd{))} -\end{alltt} -\begin{verbatim} -## make[1]: warning: jobserver unavailable: using -j1. Add '+' to parent make rule. -\end{verbatim} - - -{\ttfamily\noindent\itshape\color{messagecolor}{\#\# Successfully compiled differential equation model from auto-generated C code.}}\begin{alltt} -\hlstd{m.Z.mkin.5} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.5, FOCUS_2006_Z_mkin,} - \hlkwc{parms.ini} \hlstd{= m.Z.mkin.4}\hlopt{$}\hlstd{bparms.ode[}\hlnum{1}\hlopt{:}\hlnum{4}\hlstd{],} - \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.mkin.5)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_11-1} - -\end{knitrout} - -The summary view of the backtransformed parameters shows that we get no -confidence intervals due to overparameterisation. As the optimized -\texttt{k\_Z3\_bound\_free} is excessively small, it seems reasonable to fix it to -zero. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlstd{m.Z.mkin.5a} \hlkwb{<-} \hlkwd{mkinfit}\hlstd{(Z.mkin.5, FOCUS_2006_Z_mkin,} - \hlkwc{parms.ini} \hlstd{=} \hlkwd{c}\hlstd{(m.Z.mkin.5}\hlopt{$}\hlstd{bparms.ode[}\hlnum{1}\hlopt{:}\hlnum{7}\hlstd{],} - \hlkwc{k_Z3_bound_free} \hlstd{=} \hlnum{0}\hlstd{),} - \hlkwc{fixed_parms} \hlstd{=} \hlstr{"k_Z3_bound_free"}\hlstd{,} - \hlkwc{quiet} \hlstd{=} \hlnum{TRUE}\hlstd{)} -\hlkwd{plot_sep}\hlstd{(m.Z.mkin.5a)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_11a-1} - -\end{knitrout} - -As expected, the residual plots for Z0 and Z3 are more random than in the case of the -all SFO model for which they were shown above. In conclusion, the model -\texttt{Z.mkin.5a} is proposed as the best-fit model for the dataset from -Appendix 7 of the FOCUS report. - -A graphical representation of the confidence intervals can finally be obtained. - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{mkinparplot}\hlstd{(m.Z.mkin.5a)} -\end{alltt} -\end{kframe} -\includegraphics[width=\maxwidth]{figure/FOCUS_2006_Z_fits_11b-1} - -\end{knitrout} - -The endpoints obtained with this model are - -\begin{knitrout} -\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe} -\begin{alltt} -\hlkwd{endpoints}\hlstd{(m.Z.mkin.5a)} -\end{alltt} -\begin{verbatim} -## $ff -## Z0_free_Z1 Z1_Z2 Z2_sink Z2_Z3_free Z3_free_sink -## 1.0000000 1.0000000 0.4634431 0.5365569 1.0000000 -## -## $SFORB -## Z0_b1 Z0_b2 Z3_b1 Z3_b2 -## 2.447138640 0.007512589 0.080007099 0.000000000 -## -## $distimes -## DT50 DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2 -## Z0 0.3042972 1.184811 0.283248 92.26476 NA NA -## Z1 1.5147787 5.031986 NA NA NA NA -## Z2 1.6413857 5.452565 NA NA NA NA -## Z3 NA NA NA NA 8.663571 Inf -\end{verbatim} -\end{kframe} -\end{knitrout} - -It is clear the degradation rate of Z3 towards the end of the experiment -is very low as DT50\_Z3\_b2 (the second Eigenvalue of the system of two differential -equations representing the SFORB system for Z3, corresponding to the slower rate -constant of the DFOP model) is reported to be infinity. However, this appears -to be a feature of the data. - -\bibliographystyle{plainnat} -\bibliography{references} - -\end{document} -% vim: set foldmethod=syntax: diff --git a/docs/articles/FOCUS_Z.toc b/docs/articles/FOCUS_Z.toc deleted file mode 100644 index ebb3b24a..00000000 --- a/docs/articles/FOCUS_Z.toc +++ /dev/null @@ -1,4 +0,0 @@ -\contentsline {section}{\numberline {1}The data}{1}{section.1} -\contentsline {section}{\numberline {2}Parent compound and one metabolite}{2}{section.2} -\contentsline {section}{\numberline {3}Including metabolites Z2 and Z3}{8}{section.3} -\contentsline {section}{\numberline {4}Using the SFORB model for parent and metabolites}{12}{section.4} diff --git a/docs/articles/cache/FOCUS_2006_Z_fits_10_ad34939f1c4da097e64c6add505f564d.RData b/docs/articles/cache/FOCUS_2006_Z_fits_10_ad34939f1c4da097e64c6add505f564d.RData deleted file mode 100644 index 53e2a7d5..00000000 Binary files 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-1,6 +0,0 @@ -base -knitr -minpack.lm -rootSolve -inline -mkin diff --git a/docs/articles/compiled_models.html b/docs/articles/compiled_models.html index ce149bc5..31340867 100644 --- a/docs/articles/compiled_models.html +++ b/docs/articles/compiled_models.html @@ -16,14 +16,27 @@
## Unit: milliseconds
 ##                   expr       min        lq      mean    median        uq
-##  deSolve, not compiled 6341.1795 6363.5977 6373.7748 6386.0158 6390.0724
-##       Eigenvalue based  907.1699  908.8498  921.8335  910.5297  929.1653
-##      deSolve, compiled  747.5311  752.3718  754.2086  757.2125  757.5474
+##  deSolve, not compiled 6559.0772 6574.0500 6642.0659 6589.0229 6683.5603
+##       Eigenvalue based  921.0723  931.1284  940.3973  941.1845  950.0598
+##      deSolve, compiled  736.6534  741.6706  756.3600  746.6878  766.2132
 ##        max neval cld
-##  6394.1290     3   c
-##   947.8008     3  b 
-##   757.8823     3 a
+## 6778.0978 3 c +## 958.9351 3 b +## 785.7386 3 a
autoplot(mb.1)

-

We see that using the compiled model is by a factor of 8.4 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs:

+

We see that using the compiled model is by a factor of 8.8 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs:

rownames(smb.1) <- smb.1$expr
 smb.1["median"]/smb.1["deSolve, compiled", "median"]
##                         median
-## deSolve, not compiled 8.433585
-## Eigenvalue based      1.202476
+## deSolve, not compiled 8.824334
+## Eigenvalue based      1.260479
 ## deSolve, compiled     1.000000
@@ -113,19 +126,19 @@ smb.1["median"]/smb
smb.2 <- summary(mb.2)
 print(mb.2)
## Unit: seconds
-##                   expr       min        lq      mean    median        uq
-##  deSolve, not compiled 13.214250 13.248908 13.384577 13.283565 13.469740
-##      deSolve, compiled  1.303868  1.307484  1.332879  1.311099  1.347384
+##                   expr       min        lq      mean   median        uq
+##  deSolve, not compiled 13.587184 13.616178 13.673277 13.64517 13.716324
+##      deSolve, compiled  1.307508  1.317114  1.337594  1.32672  1.352637
 ##        max neval cld
-##  13.655915     3   b
-##   1.383669     3  a
+## 13.787476 3 b +## 1.378553 3 a
smb.2["median"]/smb.2["deSolve, compiled", "median"]
##   median
 ## 1     NA
 ## 2     NA
autoplot(mb.2)

-

Here we get a performance benefit of a factor of 10.1 using the version of the differential equation model compiled from C code!

+

Here we get a performance benefit of a factor of 10.3 using the version of the differential equation model compiled from C code!

This vignette was built with mkin 0.9.44.9000 on

## R version 3.3.2 (2016-10-31)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
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index 67dc3623..fc39bfda 100644
--- a/docs/articles/mkin.R
+++ b/docs/articles/mkin.R
@@ -2,33 +2,3 @@
 require(knitr)
 opts_chunk$set(engine='R', tidy=FALSE)
 
-## ---- echo = TRUE, cache = TRUE, fig = TRUE, fig.width = 8, fig.height = 7----
-library(mkin)
-# Define the kinetic model
-m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
-                         M1 = mkinsub("SFO", "M2"),
-                         M2 = mkinsub("SFO"),
-                         use_of_ff = "max", quiet = TRUE)
-
-
-# Produce model predictions using some arbitrary parameters
-sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
-  c(k_parent = 0.03,
-    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
-    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
-  c(parent = 100, M1 = 0, M2 = 0),
-  sampling_times)
-
-# Generate a dataset by adding normally distributed errors with
-# standard deviation 3, for two replicates at each sampling time
-d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
-                             sdfunc = function(x) 3,
-                             n = 1, seed = 123456789 )
-
-# Fit the model to the dataset
-f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
-
-# Plot the results separately for parent and metabolites
-plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
-
diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index 8134287b..49c0389b 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -1,5 +1,5 @@
 
-mkin - Kinetic evaluation of chemical degradation data • mkinIntroduction to mkin • mkin
@@ -16,14 +16,27 @@