SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networks

Abstract

Background: The size and complexity of published biochemical network reconstructions are steadily increasing, expanding the potential scale of derived computational models. However, the construction of large biochemical network models is a laborious and error-prone task. Automated methods have simplified the network reconstruction process, but building kinetic models for these systems is still a manually intensive task. Appropriate kinetic equations, based upon reaction rate laws, must be constructed and parameterized for each reaction. The complex test-and-evaluation cycles that can be involved during kinetic model construction would thus benefit from automated methods for rate law assignment.

Results: We present a high-throughput algorithm to automatically suggest and create suitable rate laws based upon reaction type according to several criteria. The criteria for choices made by the algorithm can be influenced in order to assign the desired type of rate law to each reaction. This algorithm is implemented in the software package SBMLsqueezer 2. In addition, this program contains an integrated connection to the kinetics database SABIO-RK to obtain experimentally-derived rate laws when desired.

Conclusions: The described approach fills a heretofore absent niche in workflows for large-scale biochemical kinetic model construction. In several applications the algorithm has already been demonstrated to be useful and scalable. SBMLsqueezer is platform independent and can be used as a stand-alone package, as an integrated plugin, or through a web interface, enabling flexible solutions and use-case scenarios.

Fig. 1

Architecture of SBMLsqueezer 2. An important design principle of the program is to be compatible with various frameworks. To this end, the program is modularized in three layers. The first layer is the user interface. This layer allows users to utilize the program in multiple ways, including a stand alone version with an own GUI that can also be launched from Garuda’s dashboard [24], a fully featured command-line interface, as a plugin of CellDesigner [21], or as an online program in Galaxy [22]. The web version of the program enables users to easily build complex workflows with other programs in the Galaxy framework. Similar pipelines can be achieved when using SBMLsqueezer as a Garuda gadget. No matter how the program is launched, each mode has access to the identical algorithms and program infrastructure in the second layer. The only exception is that the SABIO-RK [10] has been deactivated in the CellDesigner plugin because CellDesigner provides its own module for this purpose [8]. For software developers, this second layer can be accessed directly through its API. Hence, the algorithms can be embedded in more complex processes and be used as a module in third-party programs. The third layer contains the data structures. SBMLsqueezer highly relies on the library JSBML [18] for model representation. When being used as a plugin from CellDesigner or with libSBML [20] as model parsing and writing engine, an additional synchronization step is required: In both cases all data structures that the program receives from either CellDesigner or libSBML are mapped to a corresponding JSBML representation. All changes made by the program must then be reported to the original source

Fig. 2

Examples for general reaction categories. This figure displays example reactions in SBGN for each of the twelve categories that are used to determine applicable rate equations. a) Reaction with a non-enzyme catalyst. The ion I1 catalyzes this association reaction, which can therefore not be considered enzyme catalyzed. In addition, this reaction is also modulated in a feedback inhibition loop, has an integer stoichiometry, and two reactants. b) Gene-regulatory processes. Reaction re2a assembles an mRNA molecule from a source of bases (transcription), enabled by the a specific gene. This mRNA in turn (re2b) enables the assembly of a protein from a source of amino acids (translation). In a feedback inhibition loop, the protein interferes with the transcription of its own gene. c) Uni-uni enzyme reaction. This schematic conforms the classical Michaelis-Menten mechanism. d) Bi-uni enzyme reaction. This association reaction has an integer stoichiometry. e) Bi-bi enzyme reaction. In this example, two molecules of identical type act as reactants and also as products, respectively. f) Arbitrary enzyme reaction. This reversible reaction involves a feedback inhibition and a complex stoichiometry, in which an ion and two identical molecules are created from two distinct reactants. g) Integer stoichiometry. This reversible, enzyme-catalyzed reaction has two identical reactants and one product. h) Irreversible reaction. This reaction has no explicit catalyst assigned to it. Depending on user-settings, the algorithm can still consider this an enzyme-catalyzed reaction, assuming that the omission of the catalyst is for the sake of simplicity. i) Modulated reaction. Both, a stimulator and an inhibitor interfere with this reaction. j) Reversible reaction. This dissociation reaction can also be seen as an association when the equilibrium shifts to the reverse reaction. k) Zeroth reactant order reaction. The two product molecules lower the velocity of their own creation. l) Zeroth product order reaction. The reactant stimulates its own degradation

Fig. 3

Reaction context dialog of SBMLsqueezer 2. When using SBMLsqueezer as a stand-alone program, this dialog pops up upon right-clicking on a reaction in the model data structure. All available kinetic equations that can be potentially applied to the selected reaction are listed and can be selected via radio buttons. A tool-tip displays detailed information about each rate law and an equation renderer displays a preview of the equation. Furthermore, this dialog also provides a few particularly important settings: a) it allows users to choose whether newly generated parameters should be created as local parameters within the kinetic law or global model parameters, b) if the reaction’s directionality should be changed, and c) if the reaction should be considered an enzyme-catalyzed reaction. In situations where a catalyst is assigned to the reaction that is recognized as an enzyme (see Table 3) or as a non-enzyme this option will not be accessible. The model used in this example is described in [77]

Fig. 4

Abstract syntax tree for an enzymatic rate law for non-modulated unireactant enzymes (SBO:0000326). This tree has been constructed for the phosphoglucomutasereaction in model iJO1366 [69], in which \textsc{d}-glucose1-phosphate (g1p) is reversibly converted to \textsc{d}-glucose6-phosphate (g6p). The program internally constructs all equations in form of syntax trees, which can contain references to objects in the SBML document. In this example, the tree contains the parameters v _m+ and v _m− for the forward and reverse maximal reaction velocity (both in mol ·s ⁻¹), K _M1 and K _M2 for the Michaelis constants of the reactant and product (both in mol), the plain numerical value 1 (dimensionless in SBML Level 3, unit undefined for earlier versions of SBML), as well as references to the species g1p and g6p (both in mol). All internal nodes represent mathematical operators