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Using Constant Amount and Boundary Condition for Species

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Definition of Constant and Boundary Properties Changing Species Amounts with Reactions or Rules Keeping Species Amount Unchanged Constant = NO, Boundary = YES Constant = YES, Boundary = YES Model Edges

Definition of Constant and Boundary Properties

There are two properties (constant amount, boundary condition) to specify how the amount of a species changes or does not change during a simulation. Based on the conditions of your model you can decide how to use these properties.

The SBML specification (Level 2, Version 1) added the property BoundaryCondition to the model definition.

Species with BoundaryCondition = Yes — The species amount is either constant or determined by a rule, but in either case the amount is not determined by a chemical reaction. In other words, the simulation does not create a differential rate term from the reactions for this species even if it is in a reaction, but it can have a differential rate term created from a rule.

Species with ConstantAmount = No — The species amount is determined by a reaction or a rule, but not both.

Species with ConstantAmount = Yes — The species amount does not change during a simulation. The species can be in a reaction or rule, but it cannot have a rule that changes its amount.

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Changing Species Amounts with Reactions or Rules

Set Constant = NO, Boundary = NO

The value of a species can change, and it can change with either a reaction or rule, but not both

Constant	Boundary	Reaction	Rule	Changed By
NO	NO	YES	NO	Reaction
NO	NO	NO	YES	Rule

Example 1 — Species A is in a reaction, and it is in the reaction rate equation. The species amount or concentration is determined by the reaction. This is the most common category of a species. A differential rate equation for the species is created from the reactions.

     reaction: A -> B
reaction rate: k*A

Example 2 — Species E is not in the reaction, but it is in the reaction rate equation. E varies with another reaction or rule.

     reaction: S -> P
reaction rate: kcat*E*S/(Km + S)

Example 3 — Species G is not in a reaction, and it is not in a rate equation. G varies with an algebraic rule or rate rule.

    rate rule: dG/dt = k

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Keeping Species Amount Unchanged

Set Constant = YES, Boundary = NO

The value of a species cannot change. When a species has its ConstantValue selected and BoundaryCondition not selected, it acts like a parameter. It cannot be in a reaction and it cannot be varied by a rule.

Constant	Boundary	Reaction	Rule	Changed By
YES	NO	NO	NO	Never

Example — Species E is not in the reaction, but it is in the reaction rate equation. E is constant and could be replaced with the constant Vm = k2*E.

     reaction: S -> P
reaction rate: kcat*E*S/(Km + S)

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Constant = NO, Boundary = YES

The value of a species can change, and it is in a reaction, but a differential rate term from the reaction is not created. The value of the species change with a rule and a differential rate term is created from the rule.

Constant	Boundary	Reaction	Rule	Changed By
NO	YES	YES	YES	Rule

From the SBML specification (Level 2, Version 1), "By default, when a species is a product or reactant of one or more reactions, its concentration is determined by those reactions. In SBML, it is possible to indicate that a given species' concentration is not determined by the set of reactions even when that species occurs as a product or reactant; i.e., the species is on the boundary of the reaction system but is a component of the rest of the model."

Example 1 — Species A is not changed by the rate equation, but changes according to a rate rule. However, A could be in the rate equation that changes other species in the reaction.

     reaction: A -> B
reaction rate: k1 or k1*A
    rate rule: dA/dt = k2*A (solution is  A = k2*t)
               (enter in SimBiology as A = k2*A)

Example 2 — Species A is not in the rate equation, but changes according to an algebraic rule.

      reaction: A -> B + C
 reaction rate: k or k*A
algebraic rule: A = 2*C 
                (enter in SimBiology as 2*C - A)

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Constant = YES, Boundary = YES

The value of the species cannot change. It is in a reaction, but a differential rate term is not created from the reaction. The differential rate term is created from a rule.

Constant	Boundary	Reaction	Rule	Changed By
YES	YES	YES	NO	Never

During simulation, a differential rate equation is not created for the species. dSpecies/dt does not exist.

Example 1 — A is a infinite source and its amount does not change. B increases with a zero order rate (k and k*A are both constants). A source refers to a species where mass is added to the system.

     reaction: A -> B
reaction rate: k or k*A

Example 2 — B decreases with a first-order rate, but A is an infinite sink and its amount does not change. A sink refers to a species where mass is subtracted from the system.

     reaction: B -> A
reaction rate: k*B

Example 3 — The null species is a reserved species name that can act as a source or a sink.

     reaction: null -> B
reaction rate: k

     reaction: B -> null
reaction rate: k*B

Example 4 — ATP and ADP are in the reaction and have constant values, but they are not in the reaction rate equation.

     reaction: S + ATP -> P + ADP
reaction rate: Vm*S/(Km + S) 

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Model Edges

As you build complex models from simpler pathways, there are edges in the model that you need to define before simulating the model. Knowing where the model edges are located is important because a species that is initially constant or unregulated can later vary as you add details to your model. The concept of a model edge overlaps with SBML boundaries, but not always.

Model edge — Species with constant amounts that might or might not be modeled in the reaction and reaction rate equations. Examples are cofactors, NAD⁺, ATP, and DNA.

Model edge — Enzymes with constant amounts that are not regulated. For example, a Michaelis-Menten rate equation with Vmax specified as a parameter assumes that the amount of enzyme catalyzing the reaction remains constant.

You may want to temporarily model a regulated enzyme in a rate equation. If the amount of enzyme is constant, then this species is a model edge. After adding the reaction(s) that change the amount of the enzyme,

Model edge — Null or source species that synthesizes another species at a constant rate (zero order reaction). Mass is added to the system.

Model edge — Degradation of a species to a null or sink species (first-order reaction). Mass is taken away from the system.

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Evaluation of Reaction Rate

Scoping Parameters for Reactions, Rules, and Events

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