Bioinformatics Advance Access originally published online on September 9, 2004
Bioinformatics 2005 21(3):357-363; doi:10.1093/bioinformatics/bti018
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Bioinformatics vol. 21 issue 3 © Oxford University Press 2005; all rights reserved.
Simulation tools for biochemical networks: evaluation of performance and usability
Institute of Signal Processing, Tampere University of Technology P.O. Box 553, 33101 Tampere, Finland
*To whom correspondence should be addressed.
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Abstract |
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 TOP Abstract 1 INTRODUCTION2 SIMULATION TOOL SURVEY3 CASE STUDY4 SIMULATION RESULTS5 DISCUSSION AND CONCLUSIONSREFERENCES |
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Motivation: Simulation of dynamic biochemical systems is receiving considerable attention due to increasing availability of experimental data of complex cellular functions. Numerous simulation tools have been developed for numerical simulation of the behavior of a system described in mathematical form. However, there exist only a few evaluation studies of these tools. Knowledge of the properties and capabilities of the simulation tools would help bioscientists in building models based on experimental data.
Results: We examine selected simulation tools that are intended for the simulation of biochemical systems. We choose four of them for more detailed study and perform time series simulations using a specific pathway describing the concentration of the active form of protein kinase C. We conclude that the simulation results are convergent between the chosen simulation tools. However, the tools differ in their usability, support for data transfer to other programs and support for automatic parameter estimation. From the experimentalists’ point of view, all these are properties that need to be emphasized in the future.
Contact: antti.pettinen{at}tut.fi
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1 INTRODUCTION |
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TOPAbstract1 INTRODUCTION2 SIMULATION TOOL SURVEY3 CASE STUDY4 SIMULATION RESULTS5 DISCUSSION AND CONCLUSIONSREFERENCES |
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In recent years, many researchers have become interested in combining experimental and computational techniques in cell biology. Several tools have been designed and implemented for modeling and simulation of the signal transduction and metabolic functions of the cell. Increasing availability of biochemical data and the complexity of cellular functions are making the integrative approaches of systems biology even more important in the future.
In the simulation tools, the cellular reactions are typically described by sets of differential equations, but simple algebraic equations can also be used. The equations are solved using numerical integration methods, presuming all the model parameters possess predefined values. Only a few of the present simulation tools provide automatic parameter estimation procedures. This feature is useful if the predefined parameter values require further adjustment, or specific parameter values are unknown. Of the many simulation tools, E-CELL (Tomita et al., 1999) Virtual Cell (Schaff et al., 1997; Schaff and Loew, 1999), Gepasi (Mendes, 1993, Mendes, 1997]; [Mendes and Kell, 1998), GENESIS (Bower and Beeman, 1998; Wilson et al., 1989) combined with Kinetikit (Bhalla and Iyengar, 1999; Bhalla, 2001, 2002) and/or Chemesis Blackwell and Hellgren-Kotaleski, 2002 and Jarnac combined with JDesigner (Sauro, 2000, Sauro, 2001, www.sys-bio.org) have probably been the most extensively developed and used. In some cases, specific research interests of the group developing the software have heavily influenced the development of the simulation tool.
The available simulation tools clearly differ in their suitability for a specific type of modeling. The way of implementing a simulation model also varies between tools. The usability of any specific tool is influenced by the availability of the required operating system, manuals and online help, the selection of graphical interface versus script language, license agreements and so on. Hence, it is of interest to evaluate the properties of simulation tools. Unbiased information on qualitative evaluation and benchmarking of the simulation tools make the selection of a proper tool, or the development of a new one, easier. This paper provides evaluations of four biochemical simulation tools. In addition, this study supports the future development of simulation tools for biochemical networks.
This paper is organized as follows. First, we introduce a qualitative comparison of the four selected simulation tools. Second, we present some time series simulation results using a specific signaling pathway as a test case. Finally, we conclude the evaluation and simulation results and discuss the future needs.
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2 SIMULATION TOOL SURVEY |
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TOPAbstract1 INTRODUCTION2 SIMULATION TOOL SURVEY3 CASE STUDY4 SIMULATION RESULTS5 DISCUSSION AND CONCLUSIONSREFERENCES |
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The survey is conducted by collecting information of existing simulation tools from publications and their respective websites. For each tool, the publicly available documentation and their possible publications are studied and the tool is investigated. Some of the tools found are either fully commercial or their use is somehow restricted to a specific group. Such simulators are not tested.
Owing to the novelty of the interdisciplinary research area, all the terminology is not yet well-established. In this paper, we define a biochemical network to consist of various pathways such as metabolic and signal transduction pathways or gene regulatory pathways. Furthermore, we define a simulation tool as a software capable of time series simulation of predefined mathematical models. A design tool, on the other hand, can be used for graphically constructing a model. Most simulation tools have an integrated design tool, or models can be implemented via specific script or markup language (similar to programming languages). Examples of such simulation tools are E-Cell Tomita et al., 1999 and Jarnac/JDesigner (Sauro, 2000, 2001). Using this terminology, we thus omit the so-called modeling tools that refer to a variety of tools intended for different purposes.
A summary of the survey is presented in Table 1. The four simulation tools selected are GENESIS/Kinetikit, Jarnac/JDesigner, Gepasi and SimTool Aho, 2003. Some clarifications of the attributes are as follows:
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- Applicability describes the main application area of the simulator. All listed simulators are suitable for simulating the time series behavior of biochemical networks.
- Usability describes how easy the software is to learn and what kind of problems, if any, occur during testing. In particular, the user interface is evaluated since it is part of the program that is visible to the user. The target group being bioscientists, presumably with basic knowledge of computers, the user interface should be illustrative and easy to use. This lowers the threshold of adapting to a new software. A graphical user interface (GUI) is almost a necessity.
- Benefits and drawbacks present our views of the best and worst properties of each program. In addition to usability, we consider reliability and compatibility as the most important values.
- Registration and availability of manuals. Most of the programs are freely available, but a few of the more than 20 tools studied require registration. In some cases, the registration is carried out by applying for a right of use.
- Parameter estimation corresponds to the possibility of computational estimation of model parameter values (model fitting).
- Usability describes how easy the software is to learn and what kind of problems, if any, occur during testing. In particular, the user interface is evaluated since it is part of the program that is visible to the user. The target group being bioscientists, presumably with basic knowledge of computers, the user interface should be illustrative and easy to use. This lowers the threshold of adapting to a new software. A graphical user interface (GUI) is almost a necessity.
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3 CASE STUDY |
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TOPAbstract1 INTRODUCTION2 SIMULATION TOOL SURVEY3 CASE STUDY4 SIMULATION RESULTS5 DISCUSSION AND CONCLUSIONSREFERENCES |
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3.1 Test case
The protein kinase C (PKC) signaling pathway provides an interesting biological test case for the evaluation of simulators. It is known to exist in various cell types as a part of a larger signal transduction network. The network has been shown to be involved in several cellular functions, such as synaptic long-term potentiation (LTP) of neurons. Presumably, the signaling involved in LTP is a biochemical basis for memory and learning (Bliss and Collingridge, 1993; Bhalla and Iyengar, 1999).
The model (Fig. 1) describing the PKC pathway is obtained from the database of Quantitative Cellular Signaling (http://doqcs.ncbs.res.in; see also Sivakumaran et al., 2003). The model describes the concentration of the active form of the PKC (PKC a ). The model has been originally developed by Bhalla and Iyengar (1999) for a hippocampal neuron and it consists of 15 different interacting reactants (types of molecules or ions). Three of these reactants correspond to second messengers: arachidonic acid (AA), intracellular calcium (Ca2+) and diacylglycerol (DAG), all of which can activate the PKC pathway. In the simulations, different types of Ca2+ time series stimuli are used, such as a linearly increasing and a sine wave stimulus (Figs 2–4). The concentrations of DAG and AA are kept constant.
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The pathway model is described by the reactions, the reaction rates and the concentrations of the reactants. The basic mass action reaction kinetics is presented as
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where A and B are the reactants and C is the product. k 1 is the forward and k –1 the backward rate constant. The reaction presented in Equation (1) can be described as a differential equation of the form
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The complete system of Figure 1 is composed of 10 differential equations and one algebraic equation summing the effect of computational intermediates to the concentration of the active PKC.
3.2 GENESIS/Kinetikit
3.2.1 General description
GENESIS (GEneral NEural SImulation System) (Bower and Beeman, 1998; Wilson et al., 1989, www.genesis-sim.org/GENESIS) can be extended with Kinetikit GUI (Bhalla and Iyengar, 1999; Bhalla, 2001, 2002) to simulate the activities of large networks of interacting molecules. In Kinetikit, a simulation model can be implemented using the GUI or the Kinetikit script language. It may be practical to start with the GUI or to modify an example script file before familiarizing with the Kinetikit script language in more detail. In this study, versions 2.2 and 2.2.1 of the GENESIS simulator and versions 8 and 9 of the Kinetikit are used. GENESIS/Kinetikit simulator runs on UNIX and Linux platforms.
The initial values for the reactants, e.g. [A], [B] and [C] in Equation (2), can be given as concentrations or as numbers of molecules. However, all computations in Kinetikit are performed using the numbers of molecules. Kinetikit makes it possible to change simulation and plot time-steps. The simulation time-step can be either constant or variable. Variable time-step can speed up simulations in which the stimulus or the perturbation of a pathway first induces rapid, transient-like changes, followed by slower, prolonged responses. The slower the changes, the longer time-steps can be used and, the faster the simulation process. In Kinetikit, it is possible to utilize the following numerical integration methods: Exponential Euler (see MacGregor, 1987), Mixed Stochastic, Gibson–Bruck, Gillespie 1 and Gillespie 2. Runge–Kutta method is currently under development.
3.2.2 Implementation of the PKC test case
The implementation of the PKC pathway simulation model involves the following: (1) identification of the reactants and reactions; (2) defining the interactions (reactions) between the reactants (using the GUI or the script language); (3) setting up the reaction equations using reaction kinetics [e.g. see Equations (1) and (2)]; (4) setting the initial values for the concentrations of the reactants [e.g. see [A], [B], and [C] in Equations (1) and (2)]; and (5) setting up the stimulus using the GUI or by loading a file containing the stimulus protocol.
Based on our experience, special attention has to be paid to unit conversions since the Kinetikit GUI uses physiological units instead of SI units. It is also useful to check the model implementation details on the script level even though using the GUI. Kinetikit GUI is a usable extension to GENESIS although it takes some time to fully utilize it. Also, the possibility to use various types of stimuli makes Kinetikit a very suitable tool for realistic simulations.
3.3 Jarnac/JDesigner
3.3.1 General description
Jarnac (Sauro, 2000, www.sys-bio.org)/JDesigner (Sauro, 2001, www.sys-bio.org) is a combination of two tools. JDesigner is a design tool for biochemical networks. With JDesigner it is possible to define interactions between reactants using the drag-and-drop method and to apply reaction equations using reaction kinetics. After a mathematical model has been implemented, the network can be simulated and analyzed with other programs. It is recommended to use Jarnac for this purpose because both JDesigner and Jarnac support two common interfaces, Systems Biology Workbench (SBW) Hucka et al., 2001 and Systems Biology Markup Language (SBML) Hucka et al., 2003.
Jarnac is a script language capable of simulating the behavior of biochemical networks and pathways Sauro, 2000. It offers a variety of ways to simulate biochemical networks but is quite complicated to use on its own. However, Jarnac can be controlled from JDesigner. If a simulation utilizes kinetic laws that are included in Jarnac’s built-in library, Jarnac uses analytical forms of equation derivatives. This increases computational efficiency of the simulations. The equations can also be solved numerically if needed. Jarnac utilizes CVODE (initial value solver written in C, see Cohen and Hindmarsh, 1996) or LSODA (Livermore Solver of Ordinary Differential Equations, e.g. see Hindmarsh, 1983) to solve differential equations.
In this study, versions of the programs used are Jarnac 2.0 and JDesigner 1.8k and they run on Microsoft Windows platform.
3.3.2 Implementation of the PKC test case
The implementation of the PKC pathway simulation model includes the following steps: (1) designing the pathway using JDesigner; (2) converting the reaction parameters and the reactant concentrations used in the original model (http://doqcs.ncbs.res.in; see also Sivakumaran et al., 2003) to a suitable form for Jarnac simulation; (3) applying reaction equations describing reaction kinetics to the pathway model (all the common reaction equations for reaction kinetics are built-in in JDesigner); and (4) introducing a pseudoreaction representing the Ca2+ stimulus.
With Jarnac/JDesigner, we are limited only to simulating with a simple linearly increasing stimulus because it is not possible to use, for example, experimental time series data as a stimulus for a network. In total, Jarnac/JDesigner is found to be a competent software package for design and simulation purposes. Especially JDesigner is very easy and intuitive to use, although sometimes slightly unstable.
3.4 Gepasi
3.4.1 General description
Gepasi is a simulation tool intended for the simulation of chemical and biochemical systems. With Gepasi, it is possible to study kinetics, steady states and control of dynamic systems, as well as to estimate parameter values (Mendes, 1993, 1997; Mendes and Kell, 1998, www.gepasi.org). In this study, the version 3.30 is used. Gepasi can be run on both Linux and Microsoft Windows platforms.
The various features of Gepasi are easily accessible through a GUI. For example, networks can be implemented using the GUI, although design tool is not available. An extensive equation type library for reaction kinetics can be exploited, and simulations can be controlled using the GUI. Gepasi utilizes the LSODA routine (e.g. see Hindmarsh, 1983) to solve the differential equations. Many scientists have used Gepasi in their research (e.g. see Reijenga et al., 2002), and Gepasi can be considered an efficient and reliable tool.
3.4.2 Implementation of the PKC test case
In the next sections (a–c), three ways of setting up the simulation model of the PKC signaling pathway are presented:
- Whole model is implemented only with Gepasi.
- Ready-made model is imported in SBML format.
- Ready-made model is imported in SBML format, and the equation type library of Gepasi is utilized.
(a) Implementation with Gepasi only. The PKC pathway simulation model is implemented by defining the reaction equations via the GUI. Gepasi automatically determines the reactants from the equations, leaving only their numerical values to be added. Again, the reaction parameters and reactant concentrations used in the original model (http://doqcs.ncbs.res.in; see also Sivakumaran et al., 2003) are converted into a suitable form for Gepasi simulation. The implementation of a network or pathway is relatively easy, even for beginners.
The Ca2+ stimulus for the PKC pathway needs to be prepared separately. This is done by defining a pseudoreaction that describes the time series behavior of the stimulus. Unfortunately, neither the manual nor the help files provide needed instructions and therefore the setting of the stimulus is somewhat problematic and time-consuming.
(b) Model import in the SBML format. To test the SBML support of Gepasi, we import the PKC pathway model implemented in JDesigner. Gepasi reads the reaction equations from the SBML file and creates a new kinetic equation type for each of them. The created kinetic equation types are treated as user-defined, so the built-in equation type library is not utilized. The names of the created kinetic equation types consist of ‘SBML’ and of the number of the reaction in question (e.g. SBML01). Therefore, the names do not directly inform the user about the kinetic equation type of the reaction, forcing the user to examine the actual reaction equation more closely. This is not the case when using the equation type library of Gepasi, where the equation types are named after the kinetic laws (e.g. mass action, reversible Michaelis–Menten). The non-informative names of the created kinetic equation types, when importing an SBML model to Gepasi, are due to a deficiency in SBML. SBML does not provide for a kinetic equation type to be named. In fact, SBML does not use the concept of kinetic equation type at all. The actual simulation of the imported SBML model performs well. Problems may occur if an imported SBML model is saved as a Gepasi model. Sometimes the model file cannot be opened later, since the created kinetic reaction types can become non-existent.
(c) Model import in the SBML format and use of equation type library. First, the PKC model is imported in the SBML format. Second, the kinetic equation types of the imported model (e.g. SBML01) are replaced by the corresponding built-in kinetic equation types from the Gepasi equation type library. As shown in Figure 2 the simulation result is close to the result obtained in section (b), where the imported reactions are used as such. However, it seems that the reactions utilizing the built-in kinetic equation library of Gepasi (section c) are calculated slightly faster than the reactions that are imported in the SBML format (section b). The differences in efficiency may arise, for example, from difficulties of converting the equation strings provided in the SBML format to the inner data structures and functions used by the program.
3.5 SimTool
3.5.1 General description
SimTool is a tool for simulation of metabolic reactions and other biochemical processes Aho, 2003. SimTool runs on Matlab, which is a commercial, general-purpose programming environment for mathematical modeling, simulation, and data analysis (Mathworks, 2004 www.mathworks.com). Matlab can be run on various platforms, e.g. on Linux and Microsoft Windows. In addition to the use of various ready-made algorithms, Matlab enables the implementation of self-made ones. For example, the ready-made numerical integration algorithms can be easily adjusted to use constant or variable time-steps. Thus, SimTool is easily modifiable according to the user's needs. On the other hand, the modifications require programming experience in Matlab.
The GUI of SimTool can be used for running basic simulations but it does not make graphical design of biochemical networks possible. A design tool such as JDesigner, which produces files in the SBML format, can be used for such purposes. Alternatively, the setting up of a simulation model can be performed by writing specific scripts and function files. SimTool utilizes Numerical Differentiation Formulas Shampine and Reichelt, 1997 (altogether seven integration methods) to solve the differential equations. SimTool is available upon request from the authors.
3.5.2 Implementation of the PKC test case
The implementation process includes the following: (1) reusing the unit conversions mentioned earlier in this publication; (2) writing the script and function files describing the pathway; and (3) introducing the predefined Ca2+ stimulus as a pseudoreaction. With some modifications, SimTool would make the utilization of experimental Ca2+ time series data possible. Finally, the time series behavior of the PKC pathway model is simulated using the GUI of SimTool.
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4 SIMULATION RESULTS |
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TOPAbstract1 INTRODUCTION2 SIMULATION TOOL SURVEY3 CASE STUDY4 SIMULATION RESULTS5 DISCUSSION AND CONCLUSIONSREFERENCES |
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Simulation tools are run in ordinary desktop PCs on both Linux and Microsoft Windows platforms. All computers are of the same order in computational efficiency (
1.5 GHz processors and 1 GB RAM). Simulations are repeated in order to verify the obtained results. All the studied simulators produce results that are close to each other when the Ca2+ stimulus increases linearly from 0 to 5 µM during 500 s. Figure 2 presents the concentrations of the final product, active PKC, in time. GENESIS/Kinetikit and SimTool provide the same results. Similarly, simulation with Jarnac/JDesigner produces the same results as the simulation with the ready-made model imported in SBML format to Gepasi (3.4.2b; in Fig. 2: Gepasi: SBML imported). Thus, at least in this case, SBML is a proper interface between JDesigner and Gepasi. On the other hand, somewhat diverse results are obtained when comparing the simulations of the model implemented with Gepasi (3.4.2a; in Fig. 2: Gepasi) to the imported SBML model utilizing the kinetic equation type libraries (3.4.2c; in Fig. 2: Gepasi: SBML converted). The former implementation (3.4.2a) settles the active PKC on a lower concentration level compared to any other implementation. The latter implementation (3.4.2c) results in the steepest slope of the curve.
The sine wave stimulus of Ca2+ can be implemented only to GENESIS/Kinetikit, Gepasi and SimTool. Figures 3 and 4 show the concentrations of active PKC as simulated by the three tools. SimTool and GENESIS/Kinetikit produce the same results. The concentration of active PKC simulated by Gepasi settles on a slightly lower level.
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5 DISCUSSION AND CONCLUSIONS |
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TOPAbstract1 INTRODUCTION2 SIMULATION TOOL SURVEY3 CASE STUDY4 SIMULATION RESULTS5 DISCUSSION AND CONCLUSIONSREFERENCES |
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In the beginning of this study, a survey of the publicly available simulation tools intended for biochemical networks is conducted. Of the numerous software packages, GENESIS/Kinetikit, Jarnac/JDesigner, Gepasi and SimTool are examined in more detail. They are used to simulate the behavior of a specific PKC test case. The implementation of the test case, specifically the external stimulus, is not necessarily straightforward for all the tools. However, feasible implementation of the model is possible with all the four tools. The simulation results are found to be convergent for all the implementations. The small differences observed may be due to different numerical methods for solving differential equations. In this study, the following numerical integration methods are utilized: Exponential Euler method in Kinetikit, LSODA in Gepasi, LSODA or CVODE in Jarnac and Numerical Differentiation Formulas in Simtool. In Kinetikit and SimTool other numerical integration methods can also be chosen.
Although the tools are suitable for the simulation of the studied biochemical pathway, clear differences exist. Based on this study, the following ideas can be summarized.
First, the usability of the program is crucial from the user's point of view. For example, Gepasi and Jarnac/JDesigner are easy to use even for beginners, whereas SimTool requires former programming experience in Matlab environment.
Second, the lack of standards and interfaces between tools becomes evident. For example, the support of external interfaces, such as SBML, will become all the more important in the future as the amount of available data increases. In addition, the use of various biochemical and physiological units appears problematic because the manual conversion is a time-consuming process and the chance of error is significant. Such deficiencies make it more difficult to utilize the existing tools and hinder the development of the research area.
Third, the sufficient documentation and transparency of the implementation details are one of the fundamental principles of scientific practice. However, the current situation is that, in some cases, not even the information regarding the used integration method is properly provided. Open source projects (e.g. Jarnac/JDesigner) can provide solutions to the above-mentioned issues.
Fourth, simulation tools differ in their ability to utilize external stimuli. Real biological systems are not separated from their environment. These systems are controlled by different types of stimuli. Therefore, the computational models should also be able to adopt different kinds of input variables describing the stimuli. GENESIS/Kinetikit is a good example of a proper tool for this purpose.
Dynamic simulation of biochemical networks is under constant development in systems biology. For example, new algorithms are developed for simulating systems that include stochastic components (Takahashi et al., 2004; Vasudeva and Bhalla, 2004). Another challenging area is the computational parameter estimation for the models. Presently, a priori information of the parameters may be unavailable and the parameter values are adjusted either with some semi-automatic method or by manually varying them. Some of the existing simulation tools, such as Gepasi, GENESIS and SimTool, provide methods also for computational parameter estimation.
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Acknowledgments |
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This work was in part supported by the Academy of Finland (grants 79854, 80455, 104508 and 102067) and the National Technology Agency of Finland (grants 40069/02 and 40099/03).
Received on May 28, 2004; revised on August 31, 2004; accepted on September 3, 2004
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