Modeling biochemical transformation processes and information processing with Narrator

Abstract

Background: Software tools that model and simulate the dynamics of biological processes and systems are becoming increasingly important. Some of these tools offer sophisticated graphical user interfaces (GUIs), which greatly enhance their acceptance by users. Such GUIs are based on symbolic or graphical notations used to describe, interact and communicate the developed models. Typically, these graphical notations are geared towards conventional biochemical pathway diagrams. They permit the user to represent the transport and transformation of chemical species and to define inhibitory and stimulatory dependencies. A critical weakness of existing tools is their lack of supporting an integrative representation of transport, transformation as well as biological information processing.

Results: Narrator is a software tool facilitating the development and simulation of biological systems as Co-dependence models. The Co-dependence Methodology complements the representation of species transport and transformation together with an explicit mechanism to express biological information processing. Thus, Co-dependence models explicitly capture, for instance, signal processing structures and the influence of exogenous factors or events affecting certain parts of a biological system or process. This combined set of features provides the system biologist with a powerful tool to describe and explore the dynamics of life phenomena. Narrator's GUI is based on an expressive graphical notation which forms an integral part of the Co-dependence Methodology. Behind the user-friendly GUI, Narrator hides a flexible feature which makes it relatively easy to map models defined via the graphical notation to mathematical formalisms and languages such as ordinary differential equations, the Systems Biology Markup Language or Gillespie's direct method. This powerful feature facilitates reuse, interoperability and conceptual model development.

Conclusion: Narrator is a flexible and intuitive systems biology tool. It is specifically intended for users aiming to construct and simulate dynamic models of biology without recourse to extensive mathematical detail. Its design facilitates mappings to different formal languages and frameworks. The combined set of features makes Narrator unique among tools of its kind. Narrator is implemented as Java software program and available as open-source from http://www.narrator-tool.org.

Figure 1

Overview of osmoregulation in yeast (based on Figure 1 in [44]). The model depicted in the diagram shows the closed loop from the osmosensor at the membrane, via signal transduction, gene regulation of metabolism and the feedback effect of internal glycerol levels on the osmotic pressure and cellular volume [43]. The model illustrates the coupling of a biochemical (control) with a biophysical system.

Figure 2

The Co-dependence Methodology. Depiction of Co-dependence Methodology's conceptual layers and components: notation, model structure, formalism mapping and formalisms.

Figure 3

Novel aspects in the Co-dependence Notation. The diagram shows a simple model involving three biochemical species A, B and C rendered as a directed hypergraph, a bipartite graph and rendered in the Co-dependence Notation. Further the mapping of the Co-dependence Notation into the ordinary differential equation (ODE) formalism is depicted. Similar to bipartite graphs, the Co-dependence Notation comprises two different kinds of node, called species and process. Rectangles (Co-dependence Notation part at the bottom of the diagram, c and d) represent molecular species, clouds denote transformation processes, thick arrows represent material flow and thin dashed lines represent informational flow. One novel aspect in the Co-dependence Notation is the use of small, unfilled circles to label information sources i.e. to label entities that play a functional role in their associated process. Consequently a thick arc in conjunction with a small circle represents a co-dependency between the species and process nodes associated by the link. In this co-dependent relationship, the species influences as information source the process that is transforming the species. As indicated in the diagram sections c and d, the visual emphasis of information sources enables the mapping of the Co-dependence Notation into ODEs. A further novel aspect in the Co-dependence Notation is the optional use of information processing nodes to represent constants or computed logical entities such as rate constants, external stimuli or genetic switches. Information processing nodes also belong to the class of process nodes yet are rendered as large circles. Thus, links in Co-dependence models cannot only connect species nodes with process nodes but can also directly relate two or more process nodes with each other. This facilitates the representation of both species transformation and information processing within a single conceptual framework. The diagram section E shows how Co-dependence models decompose complex systems into simpler elements called compartments.

Figure 4

Describing the phosphorelay mechanism of the HOG signaling pathway taken from [15]. The shown Co-dependence model describes graphically the individual species and their state transitions of the phosphorelay mechanism of the yeast high osmolarity glycerol (HOG) pathway. It further describes that species SLN1 is directly affected by the concentration difference between ions in the extracellular and intracellular environment. The dependency of the process node v1 is described in detail with a sequence of processing steps involving the nodes osmoticShock, extracellularConcentration and osmolarity.

Figure 5

Describing the mitotic activation of the tyrosine kinase Src (excerpt from [16]). The process node src_activity is used to calculate the total enzymatic activity of the kinase Src, which is represented in four different phosphorylation states. The value of the src_activity node is then reused in processes that represent reactions catalyzed by this kinase, such as autophosphorylation (E), phosphorylation of PTPα (F) and Cbp (G). This graphical notation directly corresponds to the common method of modeling biochemical systems using differential-algebraic equations.

Figure 6

Describing the cycle model of Xenopus embryos taken from [17]. Different states and state transitions of CyclinE:Cdk2 dimers taken from the Cycle model of Xenopus embryos [17]. Using the auxiliary process Pool (grey shaded and replicated) to structure the use of all removed forms of Cyclin:Cdk2 dimers.

Figure 7

Typical Narrator workflow. The graphical user interface of the design tool facilitates the interactive construction and manipulation of models based on the Co-dependence Notation. The models designed with this tool conform to the syntax and semantics of the notation. Narrator can map models designed in this way to different underlying formal languages and mathematical schemes such as ODEs and simulate the models' dynamics using numerical integration. The generated data can be presented for analysis and evaluation.

Figure 8

Class diagram describing the structure of a Narrator model.

Figure 9

Animation of species nodes. Phosphorelay mechanism of the HOG signaling pathway taken from [15] with species animation. Filled species nodes indicate that they have reached their maximal concentration level relatively to their concentration development within the simulation.

Figure 10

Protein kinase C pathway taken from [27]. Left: Model of the protein kinase C pathway taken from [27]. This model was used in [26] as a test case for validating different simulation tools for biochemical networks. Right: PKC model described with Narrator.

Figure 11

Validating Narrator's Runge-Kutta 4 implementation. Simulation concentrations of active PKC using Octave and Narrator (left). The residual plot (right) shows minimal differences between the simulation results and may be due to the different numerical integration methods.

Figure 12

Modeling stimuli with Narrator. Ca2+ stimulus for the PKC pathway described with the process CAStimulus linked to the reaction R7.