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

 

University of Newcastle upon Tyne

 

MMLINK:
a program to fit the linked Michaelis-Menten type equations in this report

 

Program details

 

Contents

 

1.      Obtaining the program

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.

 

  1. As an executable, MMLINK.EXE that will run under MS-DOS or Windows: click here.
  2. As a zipped version of the same file: click here
  3. As the original FORTRAN code: click here.  Note that users are free to amend the code as they wish.  The authors give no guarantee of the correctness of the code, either before or after amendment.  Note also that the code includes publicly available subroutines written by third parties: acknowledgements of these should be made in any publications.  Details are given in the section on numerical methods.

 

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.

 

  1. ch4mm.dat:  the file containing the data to be analysed.
  2. output.txt: monitoring information about the numerical routines is in this file
  3. logfile.txt: a file containing a log of the results of the analysis.
  4. resids.dat: a file containing the residuals from fitting model II.

 

 

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.

 

  1. Double click on the icon for mmlink.exe.
  2. Open a Dos-box or Command prompt (found in Windows XP from All Programs ® Accessories). Within this window move to the correct directory and type mmlink followed by return.

 

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.

 

  • This text file contains one row for each observation.
  • The order of the rows is immaterial
  • Each row comprises three numbers and the order of these numbers within the row is critically important.
  • The numbers within each row are separated by one or more spaces.
  • The first number in each row is the substrate concentration for that observation.
  • The second number is the rate of methane production.
  • The third number is 12 or 13, indicating whether this observation corresponds to 12CH4 or 13CH4.  It is important that the third number is precisely 12 or 13.  If you enter 12.0 or 13.0 (or even 12. and 13.) then the program may fail.

 

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.