SBMLsqueezer covers various kinetic models. To decide which kinetic equation to apply to a particular reaction, each reaction is analyzed for its properties, such as reactants, products and all participating modulators.
Non-enzyme state transition reactions are modeled through generalized mass-action kinetics. Whenever this equation can be applied, SBMLsqueezer also offers the zeroth order forward or reverse mass-action kinetics, depending on the reversibility property of the reaction. SBMLsqueezer covers all special cases of this type of equation defined in the SBO besides a few irreversible rates for discrete simulation. It also allows for non-integer stoichiometries.
For enzyme-catalyzed uni-uni reactions, the user can specify whether Michaelis-Menten or convenience kinetics should be assigned. Enzymatic reactions with more reaction partners, for instance bi-bi reactions, may either be modeled using convenience or detailed ternary-complex kinetics with different reaction mechanisms, for instance random, ordered or ping-pong. For bi-uni mechanisms the kinetic equations were manually derived using the King-Altman method [23–25] (see Additional file 1 – SBMLsqueezer: Kinetic Laws). If the number of reactants or products exceeds two, then convenience kinetics is applied, which is not restricted by the number of products or reactants. All other enzyme kinetics rate laws from the SBO are implemented in SBMLsqueezer as well and appear as an alternative choice whenever the structure and the context of the reaction is adequate for the particular formula.
For gene regulatory networks, i.e., transcriptional and translational processes, the Hill equation is applied [13, 26]. SBMLsqueezer sets the boundary condition of genes automatically so that their amount cannot decrease because of transcriptional processes. If no transcriptional or translational activator participates, a basal reaction rate is assumed using a zeroth order mass-action rate law.
To incorporate control mechanisms, activation and inhibition terms were derived and integrated into the respective kinetic equations (see Additional file 1 – SBMLsqueezer: Kinetic Laws).
Since there is no specification of enzymes in the current version of CellDesigner, SBMLsqueezer allows the user to select molecule types that can act as biocatalysts. Generic and truncated proteins, RNA and complex molecules are accepted by default, but can also be deactivated. Additionally, simple and unknown molecules, 'asRNA' and receptors may in some cases be useful as enzymes. For metabolic networks, enzymatic reactions without an explicit catalyst are permitted to be treated as enzyme reactions.
Reactions with more than two reactants are unlikely to take place, therefore warnings will be given for those reactions. However, they can, depending on the context, be modeled using convenience or mass-action kinetics. Warnings are also indicated for unrealistic reactions, e.g., if transcriptional activation is assigned to a protein phosphorylation or if transcription and translation are used improperly.
Furthermore, SBMLsqueezer allows setting all reactions in the SBML file to reversible to generate all equations in a reversible manner. As Cornish-Bowden points out, this feature is often required: “Models for multi-enzyme systems must always take account of effects of products, because there is no way to ensure that product concentrations are zero in the conditions of interest [[25], pp. 312–313].”
In cases where specific equations were already assigned to some reactions SBMLsqueezer allows the user to specify if these equations should be overwritten or left unchanged.
After specifying the parameter settings, SBMLsqueezer can be invoked to generate all equations. These are displayed in a comprehensive list, which the user can alter by double-clicking on the name of any formula (see Figure 1). A specific pull-down menu containing all applicable kinetic formulas for this particular reaction allows modification of the kinetic equations of the reaction network according to the biological knowledge of the user (see Additional file 2 – SBMLsqueezer: Tutorial). The names presented in this menu are given by the SBO terms for each kinetic equation whenever the SBO contains a definition of the particular formula. In these cases the SBO identifier number also appears in the table.
Alternatively, kinetic formulas can be assigned separately to each reaction. Therefore, SBMLsqueezer provides an entry in CellDesigner's reaction context menu (see Figure 2). When called upon, SBMLsqueezer analyzes the particular reaction and provides a list of all kinetic equations that can be assigned to the given reaction and allows setting the reaction to be reversible or irreversible. When altering the reversibility property the selection of available equations may change. For the sake of simplicity, the context menu always shows the most generic names of each kinetic equation. Tool tips present the exact name of the rate law to be assigned according to the SBO or literature annotation.
After defining all rate equations, the kinetic parameters can be estimated with respect to measurement data, which often involves model optimization [12, 27–29], or can be collected from the literature and databases [30–32]. Initially, the parameters and product concentrations, in absence of user-defined values, are set to one. In contrast to the default values of zero, this allows the model to be simulated directly in CellDesigner and permits the application of a model optimization procedure.
An export function allows storing complete information about the SBML model in a comprehensive LaTeX file. After compiling to a human-readable format like PDF, an overview of all model properties is provided, including initial values of the species, parameter values, event assignments, rate laws for each species and so forth. This overview may be used to assist model development and scientific writing. This function can also be applied to models that were created with other applications and already existing kinetic equations.
