Linked Michaelis-Menten type models for
methanogenesis data
“A stable isotope titration method for measurement of
the contribution of acetate and carbon dioxide reduction to methane production”
By N.D. Gray, J.N.S. Matthews and I.M. Head
MMLINK:
a program to fit the linked Michaelis-Menten type equations in this report
Program
details
Contents
2.
Using the
program and its output
3.
Formats of files
4.
Program
restrictions
Obtaining the program
The program can be obtained
by downloading from this webpage.
Note: when
you click on the here link for a text
file, such as the FORTRAN code in 3 above, then some browsers, such as Internet
Explorer, display the file. You can then
cut and paste the contents to your computer.
Alternatively, you can download the file directly to your computer. How you do this depends on the browser you
are using. For Internet Explorer,
right-click on the link and choose Save Target As…: in Windows the usual
dialogue box appears and the file can be saved where you wish. Be careful that the saved file really has the
name you want it to have: sometimes Windows appends an extra extension to the
filename and you can end up thinking you have saved ‘mmlink.for’ and actually
have saved ‘mmlink.for.txt’ on your computer.
Using the program and its output
The program makes use of
four files. All four are plain text
files and they are named as follows.
The formats of these files
are explained below.
The program refers as
required to files with these names: the names are embedded in the program and cannot
be changed by the user. Also, the
program expects these files to be in the same directory as the program itself.
Consequently it is
recommended that the program be downloaded into an empty directory. If downloaded in zipped format, the file
ch4mm.exe should be extracted into this directory. The user then puts the data file into this
directory: if it is not already called ch4mm.dat, its name should be changed to
this.
The program is run in one of
two ways.
You will be asked for
starting values for the parameters B
and K. Guidance on how to choose these values can be
found in the section ‘How to get starting values’.
The program then calculates
likelihood ratio tests of:
i)
the hypothesis
that the residuals from observations on 12CH4 and 13CH4
have the same variance. This assesses
the adequacy of Model I relative to Model II.
If a significant P-value is found, then Model II must be used in
preference to Model I;
ii)
the hypothesis
that the total rate of methane production remains constant is assessed by
testing if C=0. This assesses the adequacy of Model II
relative to Model III. If a significant
value is found then a key assumption underlying the model is in doubt and the
user should proceed cautiously. If the
P-value is large (say P>0.1, or perhaps even P>0.05), then the data
provides no evidence against the assumption of constant methane production and
the user should be able to proceed with Model II.
The estimates of all the
parameters in Model II are then computed, along with their standard
errors. The residuals from Model II are
written to a file to allow the user to analyse separately. The percentage of total methane production
from acetoclastic methanogenesis is also computed, along with its standard
error (on the basis that Model II fits the data).
As confirmation that the
correct data have been analysed, the raw data are printed in the log file.
It is important for the user to note
that when the program MMLINK is run subsequently the three output files,
output.txt, logfile.txt and resid.dat, are overwritten. If the user is analysing a new dataset and
wants to keep the results of the previous analysis, it is essential that these
files are renamed before MMLINK is rerun.
To allow the user to check
the installation of the program, the data in the report are available in the
correct format for the program here. The logfile from fitting these data is given
below. The data are in a text file and
the comments in the Note in the above section Obtaining
the program are also relevant here.
********** MMLINK
**********
A
program to fit linked equations of Michaelis-Menten type
to data on methane production
Analysis is based on 30 data points
These are listed below in order: substrate
concentration, CH4 production rate and carbon type
0.500000 0.106373 12
0.500000 0.147284 12
0.500000 0.080546 12
0.250000 0.146240 12
0.250000 0.143175
12
0.250000 0.062654 12
0.050000 0.049859 12
0.050000 0.181081 12
0.050000 0.201099 12
0.025000 0.162355 12
0.025000 0.164929 12
0.025000 0.205022 12
0.005000 0.217967 12
0.005000 0.181625 12
0.005000 0.252819 12
0.500000 0.132074 13
0.500000 0.136658 13
0.500000 0.141296 13
0.250000 0.098007 13
0.250000 0.116628 13
0.250000 0.148249 13
0.050000 0.075231 13
0.050000 0.077191 13
0.050000 0.083336 13
0.025000 0.021732 13
0.025000 0.031391 13
0.025000 0.030095 13
0.005000 0.017368 13
0.005000 0.012958 13
0.005000 0.014305 13
Starting value for B = 0.150000
Starting value for K = 0.050000
****
Likelihood ratio tests ****
Test for equal residual variances:
likelihood ratio statistic = 36.7218 P-value = 0.0000
Test for non-constant total methane
production:
likelihood ratio statistic = 1.0528 P-value = 0.3049
**** Results from fitting Model II ****
Parameter
estimate Standard error
A 0.2294 0.0113
B 0.1521 0.0089
K 0.0623 0.0128
Residual variance for 12C data is
0.00175034
Residual variance for 13C data is
0.00017236
Percentage of contribution of acetoclastic
methanogenesis to total methane production is
100B/A
This has value 66.3% and standard error 4.9%
Formats of files
ch4mm.dat
This file contains the data
to be analysed and must be in the same directory (also known as a folder) as
the program when it is run.
output.txt
This is a plain text file
containing output from the subroutine MINIM which performs the minimisation of
the negative of the profile log-likelihoods.
The contents give information about the convergence of the simplex algorithm
which this routine implements. It can be
opened using Notepad or Wordpad or Word but few users should need to inspect
the contents of this file.
logfile.txt
This is a plain text file
containing the results of the analysis.
It can be opened using Notepad or Word.
resids.dat
This is a plain text file
containing the residuals from fitting Model II.
There is one row for each observation.
Each row contains four numbers.
The last three are the data for that observation given in ch4mm.dat, and
in the same order as in that file. The
first number in each row is the residual.
The data in this file can be read into any statistical package to allow
further analysis.
Program restrictions
The present version of the
program can analyse datasets containing a maximum of 80 data points. Note that at least three points should be
observed for each type of methane production if the program is not to
malfunction. This is not to say that a
dataset of this size is adequate, it is simply that smaller datasets will have
a very high chance of causing the program to crash.
Note: the program is the same one used to calculate the
estimates in the above report. It has
been checked carefully for this purpose with this dataset. No guarantee is given regarding the correctness
of the answers the program produces. The
FORTRAN code may be modified by the user as they wish. While the authors would be grateful to hear
of any genuine errors users believe they have encountered, they give no
undertaking to be able to fix these and cannot give advice on amendment or
development of the software.