= Practical 3: Models and their Structural Analysis =
Once again, start ScrumPy as described in the [[http://mudshark.brookes.ac.uk/Meetings/C1netWork4/ScrumPyInstall#GettingStarted|installation instructions]].

== Loading and defining models ==
 . A pre-existing model is loaded by creating an instance of a model object {{{ScrumPy.Model(model)}}} with {{{model}}} being the name of the file (string-type ending with the {{{ScrumPy}}} file extension, {{{.spy}}}, all enclosed in quotes) containing the description of the model, provided that the file is stored in the directory from where !ScrumPy was launched. If no name is provided, a GUI for selecting a model to open, is launched.

{{{#!python
>>> m = ScrumPy.Model('toy_model.spy')
}}}
 . If this  file has not yet been created, the  instruction will open a new empty  editor window. Copy  and paste the model description below.  Having done that, select  "compile" from the !ScrumPy menu in the editor, and the model is loaded.  {{{toy_model.spy}}} is the small structural model described by:

{{{
Structural()

A_tx:
    x_A -> A
    ~

R_1:
    A -> B
    ~

R_2:
    B -> C
    ~

R_3:
    C -> E
    ~

R_4:
    B -> D
    ~

R_5:
    D -> E
    ~

R_6:
    D -> F
    ~

E_tx:
    E -> x_E
    ~
}}}
 . The reactions with the suffix "{{{_tx}}}" are transporters, i.e. they convert external metabolites (with prefix "{{{x_}}}"), which can be consumed or produced, to internal metabolites, which have no net consumption or production at steady state.
 . Take a piece of paper and draw this reaction scheme as a metabolic pathway.
 . Having edited the model, before you can do any further analysis, you must tell !ScrumPy  to update the model internally by clicking the !ScrumPy/Compile menu  option. This will also save the model, and as long as you have made no  errors in entering it, you will see no further messages. You will be  informed of any errors in a pop-up window, which will tell you where the  error was first detected (not always the same as where the error is).

== Properties of structural models ==
 . The class {{{Model}}}   has a range of methods, of which some are only useful for kinetic   models (which are also structural models, but the opposite is not true).   The methods are actions on the model object ({{{m}}} in this case), and are invoked by instructions such as {{{ x = m.Method()}}}, where the outcome is a new data object {{{x}}} that contains the result.  Among the structurally relevant methods we find {{{ConsMoieties()}}} - which returns a list of conserved moieties; {{{DeadReactions()}}} - which returns a list of reactions that cannot carry steady state flux; {{{FindIsoforms()}}} - which identifies reactions from the model that are redundant, i.e. a set of reactions that have identical stoichiometry; {{{ElModes()}}} - which returns an elementary modes object; {{{Externals()}}} - which returns a list of external metabolites.

=== The stoichiometry matrix ===
 . The fields {{{Model.sm}}} and {{{Model.smx}}}   are the two stoichiometry matrices associated with a model - the  former  is the internal matrix, the latter the external. The external  matrix  contains infomation about external metabolites, whereas the  internal  does not. All instances of {{{ScrumPy}}} matrices (subclasses of {{{DynMatrix}}}) have the fields {{{cnames}}} - column names and {{{rnames}}} - row names.  Note that these are both [[Meetings/C1netWork4/Prac2#List|lists]], and can be examined as such.

{{{#!python
>>> m.sm.cnames
['R_1', 'R_2', 'R_3', 'R_4', 'R_5', 'R_6', 'E_tx', 'A_tx']
>>> m.sm.rnames                #but m.smx.rnames will be longer
['A', 'B', 'C', 'E', 'D', 'F']
}}}
 . Useful methods of {{{sm}}} (and {{{smx}}}) include {{{ReacToStr(reac)}}},

{{{#!python
>>> print m.sm.ReacToStr('R_2')
R_2:
        1/1 B -> 1/1 C
        ~
}}}
 . and  {{{InvolvedWith(name)}}},

{{{#!python
>>> m.sm.InvolvedWith('R_2')
{'C': mpq(1,1), 'B': mpq(-1,1)}
>>> m.sm.InvolvedWith('C')
{'R_2': mpq(1,1), 'R_3': mpq(-1,1)}
}}}
 . Here, 'mpq(1,1)' is the  stoichiometric coefficient for C, which for technical reasons is  represented in the model object as an arbitrary precision rational  number, i.e., 1/1 = 1, and as it is positive, C is a product.  The  coefficient for B is -1/1 = -1; it is a substrate of the reaction  because its coefficient is negative.

== Nullspace analysis ==
 . The kernel of the stoichiometry matrix can be calculated using the {{{sm.NullSpace()}}} method.

{{{#!python
>>> k = m.sm.NullSpace()
>>> k
    c_0 c_1

 R_1 -1/1  0/1
 R_2 -1/1  1/1
 R_3 -1/1  1/1
 R_4 0/1  -1/1
 R_5 0/1  -1/1
 R_6 0/1  0/1
 E_tx -1/1  0/1
 A_tx -1/1  0/1
}}}
 . Even if  the signs of some of the coefficients  indicate thermodynamically  infeasible solutions (e.g. all active  reactions in the first column  have negative coefficients, even though  they are irreversible) a lot of  useful information can be obtained form {{{k}}}. For instance, we see that the row associated with {{{R_6}}} is a null-vector, indicating that there is no steady-state solution involving {{{R_6}}}. In fact this is how {{{ScrumPy}}} detects '''''dead reactions''''' with the method {{{DeadReactions()}}}.

{{{#!python
>>> m.DeadReactions()
['R_6']
}}}
=== Enzyme subsets ===
 . Also, note that some of the row-vectors are proportional to each other - {{{R_2}}}, {{{R_3}}}; {{{R_4}}}, {{{R_5}}}; and {{{E_tx}}}, {{{A_tx}}}, {{{R_1}}}. This implies that these sets must carry flux in a coordinated fashion, e.g. any flux solution involving {{{R_4}}} must also involve {{{R_5}}}. These sets of coordinated reactions are referred to as '''''enzyme subsets''''' and can be determined using the {{{Model}}} method {{{EnzSubsets()}}}.   This method returns a dictionary object where keys are subset names  (or  reaction name if a reaction is in a singleton set) and values are   nested dictionaries where keys are reaction names and values are the   flux ratios of the reactions. The key {{{DeadReacs}}} maps to a list of dead reactions.

{{{#!python
>>> ess=m.EnzSubsets()
>>> ess
{'Ess_3': {'R_4': mpq(-1,1), 'R_5': mpq(-1,1)}, 'Ess_2': {'R_2': mpq(1,1), 'R_3': mpq(1,1)}, 'Ess_1': {'E_tx': mpq(1,1), 'R_1': mpq(1,1), 'A_tx': mpq(1,1)}, 'DeadReacs': {'R_6': mpq(1,1)}}
}}}
=== Elementary modes ===
 . The elementary modes of a model can be analysed using the method {{{Model.ElModes()}}}. This method returns an object that collects methods and fields related to the elementary modes of a given model. The member, {{{.mo}}}, is a matrix similar to {{{k}}}.

{{{#!python
>>> elmo = m.ElModes()
>>> elmo.mo
    ElMo_0 ElMo_1

 R_1 1/1  1/1
 R_2 1/1  0/1
 R_3 1/1  0/1
 R_4 0/1  1/1
 R_5 0/1  1/1
 R_6 0/1  0/1
 E_tx 1/1  1/1
 A_tx 1/1  1/1
}}}
 . The relationship between modes and metabolites is stored in the {{{sto}}} matrix.

{{{#!python
>>> elmo.sto
    ElMo_0 ElMo_1

 x_A -1/1  -1/1
 A 0/1  0/1
 B 0/1  0/1
 C 0/1  0/1
 E 0/1  0/1
 D 0/1  0/1
 F 0/1  0/1
 x_E 1/1  1/1
}}}
 . The methods {{{Modes()}}} and {{{Stos()}}} return strings with with same information as the matrices above.

{{{#!python
>>> print elmo.Modes()
ElMo_0, 1/1 E_tx, 1/1 R_1, 1/1 R_2, 1/1 R_3, 1/1 A_tx

ElMo_1, 1/1 E_tx, 1/1 R_1, 1/1 A_tx, 1/1 R_4, 1/1 R_5

>>> print elmo.Stos()
ElMo_0:
        1/1 x_A -> 1/1 x_E
        ~
ElMo_1:
        1/1 x_A -> 1/1 x_E
        ~
}}}
=== Further Properties of the  Stoichiometry Matrix and Null-space ===
 . '''(a)''' Generate a kernel of the stoichiometry matrix (using the {{{.NullSpace()}}} method described above).
 . '''(b)''' Multiply the stoichiometry matrix by the kernel matrix, using the {{{.Mul()}}} method of the stoichiometry matrix.
 . '''(c)''' Repeat the multiplication above using the external stoichiometry matrix instead.
 . '''(d)''' Create a kernel of the external stoichiometry matrix - what is different?
 . '''(e)''' Multiply the internal and external stoichiometry matrices by your new kernel.
 . '''(f)''' Try adding or removing reactions from the model, and repeat the exercises above, explain the new results.

== Further information ==
 . More details and explanation of how ScrumPy works can be found in the [[ScrumPy/Doc|documentation]], sections 2 and 3.