<!--Version 1.6 from 17\ Dec\ 2025 -->
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Network Elements
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
  <!--
      
    Reactions may either have partial kinetic information given by
    modifiers of different types (activator, inhibitor, etc) or
    have complete kinetic information given by some kinetic law, i.e.
    some arthmetic expression.
  --> 

  <!--
      A reaction network may contains four kinds of species elements: 
  (algebraic or differential) species, metabolites, proteins, and
  actors.
  --> 

  
    <!ENTITY % species-elements "
      species
    | metabolite 
    | protein 
    | actor     ">
  

    <!--
      
    Beside of the set of species elements, a network
    contains a set of edge clusters refering
    to species elements, reactions (including context inflows and outflows),
    macros for expressions, definitions of functions,
    (control) parameters, and events.	  
  --> 

  
    <!ELEMENT network (( comment
    | %species-elements;
    | reaction
    | context
    | edgecluster
    | expression
    | function
    | parameter 
    | event )*) >
  

  <!--
       A network may have an identfier with a latex-look, a kind, and a
  scale for its graph, a name, a source, and a network-version.--> 
  
  
    <!ATTLIST network
        id                        CDATA   #IMPLIED
        file                       CDATA  #IMPLIED
        latex-look          CDATA   #IMPLIED
        kind                    CDATA   #IMPLIED
        scale                   CDATA   #IMPLIED
        name                   CDATA   #IMPLIED
        source                 CDATA   #IMPLIED
        biomodels           CDATA   #IMPLIED
        csbml-version     CDATA   #IMPLIED
        network-version CDATA   #IMPLIED>
  
  
   <!-- @id  the identifier is relevant when referening to the              networks entities withing latex[tikz], -->

   <!-- @scale  the scale is a positive real number that permits to               scale the x-axis and y-axis simultaneously, -->

   <!-- @kind  is an identifier which serves for debugging purposes. -->


    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Graph Elements
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
    <!--
      
    The graph of the network contains various kinds of nodes that
    must have an identifier. --> 
  
    <!ENTITY % node "
    id                 CDATA     #REQUIRED
    latex-look   CDATA     #IMPLIED
    x                  CDATA     #IMPLIED
    y                  CDATA     #IMPLIED
    initial          CDATA      #IMPLIED
    initial-expression   CDATA    #IMPLIED
    comment     CDATA     #IMPLIED
    aux              CDATA    #IMPLIED 
    epsilon        CDATA    #IMPLIED 
    ">
  
  
  <!--
      
    Nodes have the follwoing attributes (where x-axis and y-axis
    should be given):
  -->  

   <!-- @id  identifier, -->

   <!-- @latex-look  latex display of the species' id -->

   <!-- @x  coordinate of x-axis, -->

   <!-- @y  coordinate of y-axis, -->

   <!-- @initial  an initial value for time point zero -->

   <!-- @initial-expression  the identifier of        some expression macro.        This serves for defining the initial value of a        species in dependence from the initial        values of other species -->

   <!-- @comment  a latex comment. -->

   <!-- @aux   -->

   <!-- epsilon   -->

  <!--
      
    Constraints:
  --> 
  <!--  °  the value of @x must be castable to xs:float  °  the value of @y must be castable to
    xs:float   ° 
      @initial and @initial-expression  cannot coexist a the same time.
     °  The value of 
    @initial-expression must be the @id
    of some macro expression that
    is defined in a non-cyclic manner, so that it can be evaluated
    to a number at initial time point 0.
    -->
  
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Mapping Species Elements to Graph Elements
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
    <!--
      
    Each species element is mapped to a node in the graph.
    The node of a species element is drawn as circle with solid lines.
    A species element may be related to an expression for its compartment size
    and for its concentration. 
  --> 

  
    <!ENTITY % species " %node;
          compartment           CDATA  #IMPLIED
          concentration         CDATA  #IMPLIED

	  essential           CDATA  #IMPLIED 
          initialConcentration CDATA  #IMPLIED 
    ">
  
  <!--
      
    These optional attributes of species have the following meaning:
  --> 

    <!-- @compartment  
    a species may live in some compartment.
    The value of @compartment is then
    the @idof some expression macro, which specifies
    the compartment's size.
   -->

   <!-- @concentration  
    a species may have a concentration besize of
    its amount. The value of @concentration
    is the "@id" of the expression macro for its concentration. 
   -->

   <!-- @essential  
    if present, the circle around the species' node will be drawn in red. 
    It indicates that the presence of the species is
  essential for a  network to work properly.   -->

  <!-- @initialConcentration  
     Depricated. Use @initial" or
     @initial-expression" for the inital
     value (amout) of the species instead.  
   -->


  <!--
      
    Each species element may have a set of copy nodes, which are drawn as 
    dashed circles. All nodes for the same species are linked by a splitpoint,
    which also is drawn as a node. 
    
    Logically, it doesn't matter whether a species participates in a
    reaction or  one of its copies.
  --> 
  
  
    <!ENTITY % copies "(comment*,(copy+,comment*,splitpoint,comment*)?)">
    
    <!ELEMENT metabolite %copies;   >
    <!ATTLIST metabolite %species; >

    <!ELEMENT protein    %copies;>
    <!ATTLIST protein    %species;
           cluster CDATA #IMPLIED >

    <!ELEMENT actor      %copies;   >
    <!ATTLIST actor      %species; >

    <!ELEMENT species      ((kinetic-expression)?,(%copies;),(modifier)*)  >
    <!ATTLIST species       %species;
             type      CDATA   #REQUIRED>
  

  <!--
      
    Proteins may may represent clusters of proteins in
    reality. Whether this is the case, can be indicated by the presence
    attribute cluster". In this case the speciess node is drawn with a
    double-circle:
  --> 

   <!-- @cluster  the presence of this attribute           indicates a protein cluster, its value is irrelevant. -->
 

    <!ELEMENT copy        (#PCDATA) >
    <!ATTLIST copy        %node;   >
    <!ELEMENT splitpoint  (#PCDATA) >
    <!ATTLIST splitpoint
    x          CDATA     #IMPLIED
    y          CDATA     #IMPLIED
    comment    CDATA     #IMPLIED >
  
  
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Edge Clusters
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
  <!--
       Multiple edges of the network may be clustered for nicer graph  presentation.
  
  An edge cluster is represented by a node of the graph, which can be
  used everywhere in the same way as a species node can be used.  --> 
  
    <!ELEMENT edgecluster (source*)>
  

  <!--
       
    A source of an edgecluster is a species, a 
    copy of species, or an edgecluster that has an outgoing edge
    pointing to it. 
  --> 

   <!-- edgecluster  a node that clusters edges from serveral sources. -->

  
    <!ATTLIST edgecluster %node;
          type       CDATA     #REQUIRED>
  

  <!--
       
    The type of an edge cluster is the type of edges that point to it. Only edges of
    the same type can be clustered.  
  --> 

   <!-- type  
    the value is this element one of the 6 types
    of reaction complements (see the entity complement below).
   -->


  <!--
       Each source of an edgecluster must contain a reference 
  to a species --> 

  
    <!ENTITY % species-reference "	  
       spec        CDATA     #IMPLIED
       copy        CDATA     #IMPLIED
       edgecluster CDATA     #IMPLIED" >
  
  <!--
        
    The combined values of these three attributes must give reference to one or many species:
  --> 

   <!-- @spec  identfier of a species, -->

   <!-- @copy  identifier of a copy of that species, -->

   <!-- @edgecluster  reference to one species or many of them. -->


  <!--
      
    Constraints:
  --> 
    <!--  °  
	Either  @spec or @edgecluster must be present,  
       °  
	the attribute @copy is optional in the case where @spec is present.
       °  in this case, there must be some species $species with 
      $species/@id=@spec and  $species/copy/@id=@copy.
      -->
  
  
    <!ELEMENT source (#PCDATA) >
    <!ATTLIST source %species-reference; >
  
  
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Reactions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
  <!--
       
    A reaction network may have are three kinds of reactions, represented
    by the following elements:
  --> 

   <!-- reaction  a reaction (including context inflows,           context outflows, and internal reactions), -->
 
  
  <!--
       A reaction may have various the four kinds of
  modifiers given by the following elements:
  --> 
  
  
    <!ENTITY % modifier "
      modifier
    | inhibitor
    | activator
    | accelerator">
  

   <!-- modifier  a generic modifier -->

   <!-- accelerator  an accelerator speeds up the reaction, -->

   <!-- activator  an activator is an accelerator nececessary       to apply the reaction, -->

   <!-- inhibitor  an inhibitor slows down the reaction -->
  
  
  <!--
       A reaction may have three other complements beside modifers:--> 

  
    <!ENTITY % complement "
    %modifier;
    | reactant
    | product
    | product-inh">
  

   <!-- product  a product of a reaction,  -->

   <!-- reactant  a reactant  of a reaction,  -->

   <!-- product-inh  a product with an implicit       degradation reaction.  -->

  
  <!--
       A reaction may have a kinetic-expression
  which is an arithmetic expression, or a more informal
  kinetics, beside of a set of complements.
  --> 

  
    <!ELEMENT reaction ((comment)*,((kinetics)|(kinetic-expression))?,(expression|%complement;)*) >
  

  <!--
      
    Reactions are drawn as boxed nodes. The different types of reactions
    are distinguished byt three boolean attributes:
  --> 

 
    <!ATTLIST reaction %node;
    inflow         (true|yes)    #IMPLIED
    outflow       (true|yes)   #IMPLIED
    candidate    (true|yes)  #IMPLIED  >
  

  <!--
      
    A reaction may be a context inflow or a context outflow. Otherwise,
    it is called internal. The boxes of context inflow and outflow
    nodes are rounded at the  borders. 
  --> 
  <!-- inflow  if the attribute is present then it must        be equal to true and the reaction     is a context inflow. -->

  <!-- outflow  if the attribute is present, then reaction     it must be equal to true, and the     reaction is a context outflow. -->

 <!--
      
   A reaction may be a  control candidate or not.
 --> 
 <!-- candidate  if the attribute is present, the reaction     is a control candidate. -->


   <!--
      
   The fill-color of the box indicates
    whether the reaction is a control candidate:
    Conrol candidates are colored in light orange, while
    the other reaction nodes are colored in gray.
   --> 
 
  <!--
       Semantically, the idea is that some control may
    increase or increase a context inflow or knowout or knockup an
    internal reaction.
    --> 
    
  
  <!--
      The value of attribute spec of a context inflow or outflow is 
  the identifier of the interacting species:
  --> 
  
    <!ENTITY % species-identifier "
           spec      CDATA     #REQUIRED
           copy      CDATA     #IMPLIED      " >
  

   <!--
      
     Comment elements contain texts possibly mixed with references to
     species and reactions:
   --> 
  
    <!ELEMENT comment      (#PCDATA | ref)* > 
    <!ATTLIST comment 
    latex	     CDATA    #IMPLIED 
    experiment   CDATA    #IMPLIED
    prediction   CDATA    #IMPLIED >

    <!ELEMENT ref      (#PCDATA)> 
    <!ATTLIST ref
	      spec	     CDATA    #IMPLIED 
	      reaction   CDATA    #IMPLIED >

	      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Obsolet
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
  <!--
      
    Context elements are obsolet but still permitted. They should be
    modeled now by reaction elements with attributes inflow and outflow.
  --> 
  
    
    <!ELEMENT context  (input | output)> 
    <!ATTLIST context %node; >

    <!ELEMENT input   (#PCDATA)>
    <!ATTLIST input %species-identifier; >
    <!ELEMENT output  (#PCDATA)>
    <!ATTLIST output %species-identifier; >
   
  
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Network Generation
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->

    
    <!ELEMENT generate-network
           ((add-network|
             fusion|
             remove-copy|
             add-reaction)*)>
    <!ATTLIST  generate-network
       id	  CDATA             #REQUIRED 
       scale   CDATA           #IMPLIED >

    <!ELEMENT add-network  (network,(remove*))>
    <!ATTLIST  add-network
       prefix  CDATA             #IMPLIED 
       x         CDATA             #IMPLIED
       y         CDATA             #IMPLIED
       scale_x  CDATA          #IMPLIED
       scale_y  CDATA          #IMPLIED >
    <!ELEMENT remove (#PCDATA)>
    <!ATTLIST  remove
       id        CDATA             #REQUIRED >

    <!ELEMENT fusion  ((%species-elements;),(%species-elements;))>
    <!ATTLIST  fusion
       id        CDATA             #REQUIRED >

    <!ELEMENT add-reaction  ((comment)*,
                                 ((kinetics)|(kinetic-expression))?,
                                  (expression|%complement;)*)>

   <!ATTLIST add-reaction %node;
     outflow       CDATA     #IMPLIED
     inflow         CDATA     #IMPLIED
     candidate    CDATA    #IMPLIED  >
				  
     <!ELEMENT remove-copy  (#PCDATA)>
     <!ATTLIST  remove-copy
        spec        CDATA             #REQUIRED 
        copy        CDATA             #REQUIRED >
    
  
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Arithmetic Expressions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->

<!--
      
  References to real numbers (or real functions) are
  given by the following elements.
  There references to variables
  (var), reference to control parameters
  (param),
  references to
  the value of species values (conc) either concentrations of amounts,
  references to the expressions (expr),
  and references (speed) to the speed of a reaction,
  i.e. to its kinetic law given by kinetic-expression
--> 


<!ENTITY % reference " param | conc | speed | var | expr ">

	   
<!ELEMENT param  (#PCDATA)>
<!ATTLIST param
        id    CDATA     #REQUIRED
        latex-look      CDATA     #IMPLIED>

<!ELEMENT expr  (#PCDATA) >
<!ATTLIST  expr
        id          CDATA    #REQUIRED
        latex-look      CDATA     #IMPLIED>


     <!--  latex-look in var should be ignore -->
   

<!ELEMENT var  (#PCDATA)>
<!ATTLIST  var 
      id	      CDATA     #IMPLIED
      latex-look      CDATA     #IMPLIED >

<!ELEMENT conc  (#PCDATA)>
<!ATTLIST conc 
          spec    CDATA     #REQUIRED >

<!ELEMENT speed  (#PCDATA)>
<!ATTLIST speed
	  reaction    CDATA     #REQUIRED >


<!--
       An arithmetic expression sometimes defines a real number in
the simplest case. But in most cases, they define real-valued
function.
  The atomic expressions are the references above. There are 
  applications of buildin arithmetic functions mult,
  power, etc.
 The buildin functions  are named as usual
 in MathML However, they are applied with a
 simplified syntax compared to MathML without
 using any apply elements.
--> 


  <!ENTITY % expression "
          %reference; |
          constant |
	  mult|sum|divide|minus|
	  sin|cos|tan|cot|
          sinh|cosh| tanh| coth|
          floor| ceiling|
  	  log| power|
	  time | inh | delay|
	  ifthenelse |
	  apply    ">

<!ELEMENT constant  (#PCDATA)>
<!ATTLIST  constant 
	  id	      CDATA     #IMPLIED 
	  value    CDATA     #IMPLIED
	  latex-look      CDATA     #IMPLIED >

<!ELEMENT mult  (%expression;)*>
<!ELEMENT sum  (%expression;)*>
<!ELEMENT divide  ((%expression;),(%expression;))>
<!ELEMENT minus ((%expression;),(%expression;)?)>

<!ELEMENT power ((%expression;),(%expression;))>
<!ELEMENT log ((%expression;), (%expression;))>

<!ELEMENT sin (%expression;)>
<!ELEMENT cos (%expression;)>
<!ELEMENT tan (%expression;)>
<!ELEMENT cot (%expression;)>

<!ELEMENT sinh (%expression;)>
<!ELEMENT cosh (%expression;)>
<!ELEMENT tanh (%expression;)>
<!ELEMENT coth (%expression;)>

<!ELEMENT ceiling (%expression;)>
<!ELEMENT floor ((%expression;))>


<!--
       Beside of the usual building operators from MathML, there
are the following more specific operators:
--> 

<!--  ° 
    time for the identity function
   ° 
    inh for the inhibition function
    with  inh(x)=1/1+x
   ° 
    delay for delays in differential equations
   ° 
    ifthenelse for conditionals
   ° 
    apply for applying function defined in the network
    itself (rather than being buildin in MathML).
  -->


  <!ELEMENT time  (#PCDATA)>
  <!ELEMENT delay ((%expression;), (%expression;))> 
  <!ELEMENT inh (%expression;)>
  
  <!ELEMENT apply  ((%expression;)*)>
  <!ATTLIST  apply
           fun              CDATA     #REQUIRED
	   latex-look  CDATA     #IMPLIED >


 <!--
      
   Arithmetic expressions subsume conditionals ifthenelse
   that permit to define piecewise functions. They contain boolean
   expressions as conditions, which may compare 
   real numbers for equality or ordering. Furthermore,
   Boolean expressions are closed under the boolean operators.
 --> 
 

 <!ENTITY % boolexpression "eq | lt |  leq | and | or | not">

 <!ELEMENT ifthenelse
        ((%boolexpression;),(%expression;),(%expression;))>


    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Function Defintions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->


<!--
      
  Functions can be defined by using lambda expressions
  possibly binding several variables at once.
--> 


<!ELEMENT function (lambda)>
<!ATTLIST  function %node;>

<!ELEMENT lambda ((bvar | %expression;)*)>
<!ELEMENT bvar  (#PCDATA)>
<!ATTLIST  bvar 
	  id	      CDATA     #IMPLIED >


<!--
       A reaction may have a kinitic law that is described by the element
  kinetic-expression and defined by some artihmetic expression:
--> 


    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Kinetic Laws
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
  
<!ELEMENT kinetic-expression (%expression;)>
<!ATTLIST  kinetic-expression 
        angle      CDATA     #IMPLIED >
  
  
<!--
       
  A way to describe kinetics in a partial manner is by using the
  element kinetics instead of
  kinetic-expression. This method is depricated.
  Named kinetics such as mass-action can be defined by arithmetic
  functions instead.
--> 
  
           
    <!ELEMENT kinetics    (#PCDATA) >
   
    <!ATTLIST kinetics
         id        CDATA     #IMPLIED
         expr      CDATA     #IMPLIED  
         mode      CDATA     #IMPLIED
         angle     CDATA     #IMPLIED  >
  
  <!--
      
    The kinetics is described either by the identifier @id or 
    informally by the latex expression @expr. Whether the
    descriptor is exact or up to similarity is specifie by @mode.
  --> 

   <!-- @id  
    An identfier of a kinetics, which must have either of the following three values  -->
    
    <!--  °  exp :    expression kinetics with constant equal to 1
       °  ma  :   mass action kinetics with rate constant equal to 1
       °  deac:  deactivation kinetics with rate constant equal to 1 
    -->
  
     <!-- @expr  
      an arbitrary latex expression describing the kinetics.
      It may use the following predefined latex macros:
     -->

    <!--  °  \BS{...} for binding sites,  °  \Prom{...} for promoters, and  °  \Op{...} for operons. -->
    <!--
      
      Other latex macros can be user defined by addition to the file
      Graph/Latex/macros.sty.
    --> 


   <!-- @mode  
    The interpretation mode may be either modulo similarity or exact. In the
    former case, the attribute mode must be absent, in the latter it must 
    satisfy mode="equal".
   -->

   <!-- @angle  
    The attribute angle says where the descriptor of the kinetics is annotated at
    the reaction node. If the id attribute is present, then the value of
    the annotation is the value of attribute expr.
   -->


  <!--
      
    Constraints:
  --> 
    <!--  °  exactely one of the attributes @id and @expr must be present.
       °  the only possible value for @mode is equal.
       °  the only possible values for @id are exp,
      ma, and deac
    -->

    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Modifiers and Reaction Complements
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
<!--
      
  
    Reactions may have four kinds of modfiers: 
    genral modifiers, inhibitors, activators, accelerators.
  --> 
  
  
    <!ELEMENT modifier   (#PCDATA) >
    <!ATTLIST modifier    %species-reference; >
    <!ELEMENT inhibitor   (#PCDATA) >
    <!ATTLIST inhibitor   %species-reference; >
    <!ELEMENT activator   (#PCDATA) >
    <!ATTLIST activator   %species-reference; >
    <!ELEMENT accelerator (#PCDATA) >
    <!ATTLIST accelerator %species-reference; >
  

  <!--
      
    Beside of the modifiers there are three other kinds of reaction complements: 
    reactants, products, and inhibited products (hiding a degradation reaction).
  --> 
  
    <!ENTITY % reaction-complement "%species-reference;
        stoichiometry CDATA   #IMPLIED"  >
    <!ELEMENT reactant      (#PCDATA) >
    <!ATTLIST reactant      %reaction-complement; >
    <!ELEMENT product       (#PCDATA) >
    <!ATTLIST product       %reaction-complement; >
    <!ELEMENT product-inh   (#PCDATA) >
    <!ATTLIST product-inh   %reaction-complement; >
  
   <!-- @stoichiometry  
    the value of the stoichiometry attribute it is computed automatically by the implementation.
    User defined stoichiometry values will be overwritten so that they become correct if necessary.
   -->


    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Macros for  Expressions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
    <!--
       We also have expressions defined by macros. These
  can be refered to by using the tag expr.
  --> 
  
  
<!ELEMENT expression  (%expression;)>
<!ATTLIST  expression %node; >


    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Control Parameters and Events
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
<!--
       A control parameter defines a trajectory by some arithmetic expression --> 


<!ELEMENT parameter  (#PCDATA)>
<!ATTLIST  parameter %node; >


<!--
       An event has a triger condition and a set of updates --> 


  <!ELEMENT event (condition, (update)*)>
  <!ATTLIST  event 
      id	      CDATA     #IMPLIED
      latex-look          CDATA   #IMPLIED >


<!--
       An trigger condition is a conjunction of equations and inequations --> 


  <!ELEMENT condition (%boolexpression;)>
  
  <!ELEMENT eq  ((%expression;),(%expression;))>
  <!ELEMENT lt   ((%expression;),(%expression;))>
  <!ELEMENT leq ((%expression;),(%expression;))>
  <!ELEMENT and ((%boolexpression;)*)>
  <!ELEMENT or ((%boolexpression;)*)>
  <!ELEMENT not (%boolexpression;)>


<!--
       we can update the concentrations of species and the values of parameters
--> 


  <!ELEMENT update ((conc|param), (%expression;))>
  <!ATTLIST  update>