ReactionNetworks -- create chemical reaction networks and corresponding steady-state and conservation equations

Description

The ReactionNetworks package provides functions for creating the steady-state and conservation equations corresponding to a given reaction network. Included are some basic building-block motifs, which can be joined together to create specific reaction network. Examples are provided illustrating elimination and degeneration with removal of a species or a reaction and the corresponding effect on the solutions of the system.

Basic Functions: reactionNetwork, isDeficient, isWeaklyReversible, steadyStateEquations conservationEquations, glue

Motifs: oneSiteModificationA, oneSiteModificationB, oneSiteModificationC, oneSiteModificationD, twoSiteModificationE, twoSiteModificationF, twoSiteModificationG, modificationOfTwoSubstratesH, modificationOfTwoSubstratesI, twoLayerCascadeJ, twoLayerCascadeK, twoLayerCascadeL, crossLinkingModelCelldeath (missing documentation) , clusterModelCellDeath, wnt, nSiteProcessiveModification, nSiteDistributiveModification, nSiteImmuneReaction, nSiteDiffusion, nSitePoreForming, nSiteSequestration, nSiteAutocatalytic

Examples

The following example demonstrates how to compute the degree and dimension of the ideal cut out by the steady-state and conservation equations.

i1 : N = reactionNetwork "A <--> 2B, A + C <--> D, B + E --> A + C, D --> B+E"

o1 = A-->2B
     2B-->A
     A+C-->D
     D-->A+C
     D-->B+E
     B+E-->A+C

o1 : ReactionNetwork

i2 : R = createRing(N, QQ)

o2 = R

o2 : PolynomialRing

After creating the reaction network and the corresponding ring, we create the steady state equations and substitute random values for the reaction rates; this will allows us to compute the degree of the ideal.

i3 : SS = flatten entries steadyStateEquations N

        2                                                                   
o3 = {xx kk       - xx xx kk       + xx xx kk       - xx kk       + xx kk   
        B  {1, 0}     A  C  {2, 3}     B  E  {4, 2}     A  {0, 1}     D  {3,
     ------------------------------------------------------------------------
              2
       , - 2xx kk       - xx xx kk       + 2xx kk       + xx kk      , -
     2}       B  {1, 0}     B  E  {4, 2}      A  {0, 1}     D  {3, 4}   
     ------------------------------------------------------------------------
     xx xx kk       + xx xx kk       + xx kk      , xx xx kk       - xx kk   
       A  C  {2, 3}     B  E  {4, 2}     D  {3, 2}    A  C  {2, 3}     D  {3,
     ------------------------------------------------------------------------
        - xx kk      , - xx xx kk       + xx kk      }
     2}     D  {3, 4}      B  E  {4, 2}     D  {3, 4}

o3 : List

i4 : K = apply(#N.ReactionRates, i->random QQ)

      9  1  9  1     3
o4 = {-, -, -, -, 1, -}
      2  2  4  2     4

o4 : List

i5 : Rr = N.ReactionRates/value

o5 = {kk      , kk      , kk      , kk      , kk      , kk      }
        {0, 1}    {1, 0}    {2, 3}    {3, 2}    {3, 4}    {4, 2}

o5 : List

i6 : P = apply(#Rr, i->Rr#i=>sub(K#i,R))

                  9              1              9              1             
o6 = {kk       => -, kk       => -, kk       => -, kk       => -, kk       =>
        {0, 1}    2    {1, 0}    2    {2, 3}    4    {3, 2}    2    {3, 4}   
     ------------------------------------------------------------------------
                    3
     1, kk       => -}
          {4, 2}    4

o6 : List

i7 : F' = apply(SS, s-> sub(s,P))

      1  2   9         3         9      1         2   3                      
o7 = {-xx  - -xx xx  + -xx xx  - -xx  + -xx , - xx  - -xx xx  + 9xx  + xx , -
      2  B   4  A  C   4  B  E   2  A   2  D      B   4  B  E      A     D   
     ------------------------------------------------------------------------
     9         3         1     9         3       3
     -xx xx  + -xx xx  + -xx , -xx xx  - -xx , - -xx xx  + xx }
     4  A  C   4  B  E   2  D  4  A  C   2  D    4  B  E     D

o7 : List

Next, we create the conservation equations and assume there is no translation, i.e., the initial conditions are all zero.

i8 : C = conservationEquations N

o8 = {2xx  + xx  - xx  + xx  - 2cc  - cc  + cc  - cc , - 2xx  - xx  + 2xx  +
         A     B     C     D      A     B     C     D       A     B      C  
     ------------------------------------------------------------------------
     xx  + 2cc  + cc  - 2cc  - cc }
       E      A     B      C     E

o8 : List

i9 : L = {0,0,0,0,0}

o9 = {0, 0, 0, 0, 0}

o9 : List

i10 : Iv = N.InitialValues

o10 = {cc , cc , cc , cc , cc }
         A    B    C    D    E

o10 : List

i11 : S = apply(#Iv, i->R_(Iv#i)=>L#i)

o11 = {cc  => 0, cc  => 0, cc  => 0, cc  => 0, cc  => 0}
         A         B         C         D         E

o11 : List

i12 : F'' = apply(C, c->sub(c,S))

o12 = {2xx  + xx  - xx  + xx , - 2xx  - xx  + 2xx  + xx }
          A     B     C     D       A     B      C     E

o12 : List

Finally, we join the two sets of equations and create an ideal. Thus, the degree and dimension can be computed.

i13 : F = join(F',F'')

       1  2   9         3         9      1         2   3                    
o13 = {-xx  - -xx xx  + -xx xx  - -xx  + -xx , - xx  - -xx xx  + 9xx  + xx ,
       2  B   4  A  C   4  B  E   2  A   2  D      B   4  B  E      A     D 
      -----------------------------------------------------------------------
        9         3         1     9         3       3
      - -xx xx  + -xx xx  + -xx , -xx xx  - -xx , - -xx xx  + xx , 2xx  + xx 
        4  A  C   4  B  E   2  D  4  A  C   2  D    4  B  E     D     A     B
      -----------------------------------------------------------------------
      - xx  + xx , - 2xx  - xx  + 2xx  + xx }
          C     D       A     B      C     E

o13 : List

i14 : I = ideal F

             1  2   9         3         9      1         2   3               
o14 = ideal (-xx  - -xx xx  + -xx xx  - -xx  + -xx , - xx  - -xx xx  + 9xx  +
             2  B   4  A  C   4  B  E   2  A   2  D      B   4  B  E      A  
      -----------------------------------------------------------------------
             9         3         1     9         3       3
      xx , - -xx xx  + -xx xx  + -xx , -xx xx  - -xx , - -xx xx  + xx , 2xx 
        D    4  A  C   4  B  E   2  D  4  A  C   2  D    4  B  E     D     A
      -----------------------------------------------------------------------
      + xx  - xx  + xx , - 2xx  - xx  + 2xx  + xx )
          B     C     D       A     B      C     E

o14 : Ideal of R

i15 : degree I

o15 = 5

i16 : dim I

o16 = 11

Authors

Cvetelina Hill <[email protected]>
Timothy Duff <[email protected]>
Kisun Lee <[email protected]>
Anton Leykin <[email protected]>
Alexandru Iosif <[email protected]>
Michael Adamer <[email protected]>

Version

This documentation describes version 1.0 of ReactionNetworks.

Source code

The source code from which this documentation is derived is in the file ReactionNetworks.m2. The auxiliary files accompanying it are in the directory ReactionNetworks/.

Exports

Types
- ReactionNetwork -- a mutable hash table, stores information about a reaction network
Functions and commands
- clusterModelCellDeath -- an example of a chemical reaction
- conservationEquations -- creates the conservation equations of a reaction network
- createConcentrationRates -- used in creating reaction network ring
- createInitialValues -- used in creating reaction network ring
- createReactionRates -- used in creating reaction network ring
- createRing -- creates a ring with generators species concentrations, reaction rates, initial values
- crossLinkingModelCelldeath (missing documentation)
- displayComplexes (missing documentation)
- glue -- combine two networks
- isDeficient -- determines deficiency of a network
- isWeaklyReversible -- determines if a network is weakly reversible
- modificationOfTwoSubstratesH -- an example chemical reaction motif
- modificationOfTwoSubstratesI -- an example chemical reaction motif
- negativeLaplacian -- Computes the negative of the Laplacian matrix of a Reaction Network.
- negativeUndirectedLaplacian -- Computes the negative of the Laplacian matrix of an undirected graph associated with a Reaction Network.
- negativeWeightedLaplacian -- Computes the negative of the weighted Laplacian matrix of a Reaction Network.
- nSiteAutocatalytic -- A motif for autocatalytic networks
- nSiteDiffusion -- an example for a diffusion network
- nSiteDistributiveModification -- A motif for purely distributive phosphorylation
- nSiteImmuneReaction -- A motif for an immune response network
- nSitePoreForming -- an example for a pore forming network
- nSiteProcessiveModification -- A motif for purely processive phosphorylation
- nSiteSequestration -- A motif for sequestration networks
- oneSiteModificationA -- an example for chemical reaction motif
- oneSiteModificationB -- an example for chemical reaction motif
- oneSiteModificationC -- an example for chemical reaction motif
- oneSiteModificationD -- an example for chemical reaction motif
- reactantMatrix -- Computes the reactants matrix of a Reaction Network.
- reactionMatrix (missing documentation)
- reactionNetwork -- creates a reaction network
- steadyStateEquations -- creates steady-state equations of a reaction network
- stoichiometricConeKer -- Computes a matrix whose columns are the rays of the cone non-negative kernel of the stoichiometric matrix of a Reaction Network.
- stoichiometricMatrix -- Computes the stoichiometric matrix of a Reaction Network.
- stoichiometricSubspace -- Computes the stoichiometric space of a Reaction Network.
- stoichSubspaceKer -- Computes the kernel of the stoichiometric matrix of a Reaction Network.
- subRandomInitVals (missing documentation)
- subRandomReactionRates (missing documentation)
- twoLayerCascadeJ -- an example chemical reaction motif
- twoLayerCascadeK -- an example chemical reaction motif
- twoLayerCascadeL -- an example for chemical reaction motif
- twoSiteModificationE -- an example for chemical reaction motif
- twoSiteModificationF -- an example for chemical reaction motif
- twoSiteModificationG -- an example chemical reaction motif
- wnt -- shuttle model for Wnt signaling pathway
Methods
- conservationEquations(ReactionNetwork) -- see conservationEquations -- creates the conservation equations of a reaction network
- conservationEquations(ReactionNetwork,Ring) -- see conservationEquations -- creates the conservation equations of a reaction network
- createRing(ReactionNetwork) -- see createRing -- creates a ring with generators species concentrations, reaction rates, initial values
- createRing(ReactionNetwork,Ring) -- see createRing -- creates a ring with generators species concentrations, reaction rates, initial values
- glue(List,ReactionNetwork) -- see glue -- combine two networks
- glue(ReactionNetwork,List) -- see glue -- combine two networks
- glue(ReactionNetwork,ReactionNetwork) -- see glue -- combine two networks
- negativeLaplacian(ReactionNetwork) -- see negativeLaplacian -- Computes the negative of the Laplacian matrix of a Reaction Network.
- negativeUndirectedLaplacian(ReactionNetwork) -- see negativeUndirectedLaplacian -- Computes the negative of the Laplacian matrix of an undirected graph associated with a Reaction Network.
- negativeWeightedLaplacian(ReactionNetwork) -- see negativeWeightedLaplacian -- Computes the negative of the weighted Laplacian matrix of a Reaction Network.
- nSiteAutocatalytic(ZZ) -- see nSiteAutocatalytic -- A motif for autocatalytic networks
- nSiteDiffusion(ZZ) -- see nSiteDiffusion -- an example for a diffusion network
- nSiteDistributiveModification(ZZ) -- see nSiteDistributiveModification -- A motif for purely distributive phosphorylation
- nSiteImmuneReaction(ZZ) -- see nSiteImmuneReaction -- A motif for an immune response network
- nSitePoreForming(ZZ) -- see nSitePoreForming -- an example for a pore forming network
- nSiteProcessiveModification(ZZ) -- see nSiteProcessiveModification -- A motif for purely processive phosphorylation
- nSiteSequestration(ZZ) -- see nSiteSequestration -- A motif for sequestration networks
- reactantMatrix(ReactionNetwork) -- see reactantMatrix -- Computes the reactants matrix of a Reaction Network.
- reactionNetwork(Ideal) -- see reactionNetwork -- creates a reaction network
- reactionNetwork(List) -- see reactionNetwork -- creates a reaction network
- reactionNetwork(String) -- see reactionNetwork -- creates a reaction network
- steadyStateEquations(ReactionNetwork) -- see steadyStateEquations -- creates steady-state equations of a reaction network
- steadyStateEquations(ReactionNetwork,Ring) -- see steadyStateEquations -- creates steady-state equations of a reaction network
- stoichiometricConeKer(ReactionNetwork) -- see stoichiometricConeKer -- Computes a matrix whose columns are the rays of the cone non-negative kernel of the stoichiometric matrix of a Reaction Network.
- stoichiometricMatrix(ReactionNetwork) -- see stoichiometricMatrix -- Computes the stoichiometric matrix of a Reaction Network.
- stoichiometricSubspace(ReactionNetwork) -- see stoichiometricSubspace -- Computes the stoichiometric space of a Reaction Network.
- stoichSubspaceKer(ReactionNetwork) -- see stoichSubspaceKer -- Computes the kernel of the stoichiometric matrix of a Reaction Network.
- substitute(ReactionNetwork,List) -- substitute species names in reaction network
Symbols
- FullEdges (missing documentation)
- Input (missing documentation)
- NullEdges (missing documentation)
- Complexes -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- ConcentrationRates -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- InitialValues -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- NullIndex -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- NullSymbol -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- ReactionGraph -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- ReactionRates -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- ReactionRing -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network
- Species -- see ReactionNetwork -- a mutable hash table, stores information about a reaction network

For the programmer

The object ReactionNetworks is a package.