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                                         Summary of DOCSS model structure

To describe the file format, we use the following example from 3x3:


Models are classified according to classes which are specified by the name: mxn where m is the number of molecules and n the number of reactions. So 3x3 has 3 molecules and 3 reactions.

M116:  |AabX|DbaX|Jacb|  0.064  2.36  0.266  0.018  0.019  2.360  0.709  1.882  0.030

The M specifies the model number, a unique id within each class.
The section delimited by vertical bars '|' is the model signature.
This specifies the reaction configuration, the first letter of the signature specifies the reaction from the list below, and the following lower case letters identify the molecules. X indicates that the reaction only involves two molecules so there is no third entry.

a <==> bAabXConversion reaction
2a <==> bBabXConversion reaction
a --a--> bCabXEnzymatic reaction catalyzed by a
a --b--> bDabXEnzymatic reaction catalyzed by b
a <==> b + cEabcConversion reaction
2a <==> b + cFabcConversion reaction
2a + b <==> cGabcConversion reaction
2a + b <==> 2cHabcConversion reaction
4a + b <==> cIabcConversion reaction
a --b--> cJabcEnzymatic reaction catalyzed by b
a --a--> b + cKabcEnzymatic reaction catalyzed by a
a --b--> b + cLabcEnzymatic reaction catalyzed by b

All enzymatic reactions are shortcuts for a full mass-action implementation of the following two reactions

E + S <======> E.S -----> E + P
E = Enzyme
S = Substrate
P = Product.
We explicitly compute the concentration of the E.S complex, and the two reactions involving it, for every enzyme.


The value specifies the parameters of the model, in the following sequence:

First, all the molecule concentrations, in alphabetical order.
Then, each of the reaction parameters, in alphabetical order. Each reaction requires two parameters, as follows:
Conversion reaction:
Parameter 1 = Kf
Parameter 2 = Kb

Enzymatic reaction
Parameter 1 = kcat
Parameter 2 = Km
As we use an expanded form for the enzyme, we need a three parameters. These are:
         k1         k3
E + S <======> E.S -----> E + P
         k2

k1 = (k2 + k3 )/Km
k2 = 4 * kcat
k3 = kcat

      ----------------------------------------------------------------------      

State may be stable,unstable,saddle,line or doublet solution depending on the eignen values.

Zeroness specifies how many of the values in the solution vector are zero.

Multiplicity specifies how many such identical solutions turned up.


      ----------------------------------------------------------------------      

eigs:  -114.751  -0.329  -11.926

This lists the eigenvalues.
If all the eigenvalues are negative then solution will be a stable point.
If there is a single positive eigenvalue, it is a saddle.

      ----------------------------------------------------------------------      

soln:  0.008  2.302 0.027 0.209 0.057

Here we list the concentrations of the molecules at the solved steady-state.
These are in a funny order, because the solution vector includes both the main set of molecules and also the enzyme-substrate complexes.
In brief,
1. Molecules are ordered alphabetically.
2. The position of an enzyme complex is after than that of any of its
molecules, but before any later molecule.
Within this criterion, enzymes are ordered alphabetically.

In this example, |AabX|DbaX|Jacb|, the solution sequence is
a, b, DbaX_complex, c, Jacb_complex