Mass Action Reactions

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Summary  Palette

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Basic Form

The canonical form for a mass action reaction in xCellerator is

where p₁,p₂,..., q₁,q₂,..., are numbers (not symbols) representing stoichiometries, and A₁,A₂,... represent chemical species. It is interpreted as

where the product runs over all the species on the left side of the arrow, and p_i and q_i are the stoichiometries of A_i on the left-hand side and right-hand sides of the arrow, respectively.

An equivalent textual form for is ShortRightArrow[A, B].

For example:

The stoichiometries may be any combination of integers, rational, or real numbers. Variable stoichiometries are not supported. Missing rate constants default to 1:

Basic Form, Reversible

The canonical form for a reversible mass action reaction in xCellerator is

It is equivalent to the pair of reactions

Missing rate constants default to 1.

An equivalent textual form for is RightArrowLeftArrow[A, B].

Basic Form, Catalytic

The canonical form for a simple catalytic is

which is equivalent to the basic reaction

The essential observation is that the concentration of the catalyst (e.g., C does not change.

For example,

There may be multiple reactants and products (but there must be only one catalyst) and stoichiometries may be specified for the reactants and products:

An equivalent textual form for is

Overscript[ShortRightArrow[A, B], C].

Catalytic, Reactant-Enzyme Complex

The basic catalytic reaction is

and is equivalent to the following set of reactions:

where Bind[A,C] represents a complex formed by the two species A and C.

The rate constants are optional and default to k1=k2=k3=1, k4=0

The user is strongly cautioned to resist the temptation to designate the Enyzme by the variable E which represents the base of the natural logarithm in Mathematica.

An equivalent textual form for is

Overscript[RightArrowLeftArrow[A, B], C].

Example:

Reversible Catalytic, Reactant-Enzyme Complex

The reaction is equivalent to the pair of reactions It can have either six or eight rate constants.

With six rate constants,

it is interpreted in the same manner as the pair of reactions

With eight rate constants

it is interpreted in the same manner as the pair of reactions

An equivalent textual form for is

Underoverscript[RightArrowLeftArrow[A, B], ER, EF].

Example:

Two Complex Catalytic

The reaction represents the set of reactions

It should have precisely six rate constants,

representing

An equivalent textual form for is

Overscript[Equilibrium[A, B], C].

Example:

Summary of Mass Action Arrow Forms

Arrow	What it represents
	Mass action
	Mass action with specified stoichiomitries

Mass Action Palette

Mass action arrows can be selected from the mass action palette: