Bioinformatics Advance Access originally published online on March 1, 2008
Bioinformatics 2008 24(8):1112-1114; doi:10.1093/bioinformatics/btn080
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Reference descriptions of cellular electrophysiology models
Division of Bioengineering, National University of Singapore, Singapore
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Summary: In recent years there has been much development of the fundamental ideas underlying mathematical model curation in regard to models of biology. While much has been achieved in the realms of systems biology and bioinformatics, little progress has been made in relation to cellular electrophysiology modeling. The primary reason for slow progress in this field is the lack of a consistent and machine-readable reference description for a given model. CellML has been widely used to describe mathematical models of cellular electrophysiology in an unambiguous, machine-readable format. Through the use of well-annotated CellML models we propose a standard by which reference descriptions of cellular electrophysiology models can be similarly defined in an unambiguous, software independent, and machine-readable format. Adoption of this standard will provide a consistent technology by which cellular electrophysiology models can be curated.
Availability: http://www.bioeng.nus.edu.sg/compbiolab/p2/
Contact: david.nickerson{at}nus.edu.sg
Supplementary information: Example reference descriptions are available at http://www.bioeng.nus.edu.sg/compbiolab/p2/
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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There is a long history of publication of mathematical models of cellular electrophysiology, dating back to the seminal work of Hodgkin and Huxley (1952). Historically, cellular electrophysiology model developments and justifications are well specified in the model's original journal publication whereas the mathematical model itself is not always specified in such great detail. Additionally, complete parametrization and specification of required boundary conditions for particular numerical simulations using the models are not always present—often due to requirements to provide a concise description of the model in traditional journal publication formats. Furthermore, the actual numerical and computational methods used to perform simulations are generally even less well defined in the original model publication. These factors make it very difficult for scientists to accurately utilize previous work without considerable effort on their part to develop a working implementation of the model they wish to use. This approach leaves doubt as to a quantitative measure of the validity of such model implementations.
As an aid to overcome these shortcomings, model authors often use the Internet to distribute computer code for their own implementation of their model(s). A good example of this is the Rudy lab (http://rudylab.wustl.edu/), which provides source code for the widely used LRd-based model series. While useful as an aid to enable scientists to utilize mathematical models, there is usually no direct relationship between a model's publication and any provided code. As such, there is still no easy way to check a new implementation of the model or quantitatively compare the model's implementation with results from the model's original publication. An example of this is when such models must be re-implemented in a specific format for inclusion in other tools, such as the use of LRd models in whole heart electrophysiology modeling.
In the field of systems biology, much effort has been invested in creating validated and curated models, such that models can be reused and combined in new ways (see, for example, http://www.biomodels.net). The MIRIAM standard (Le Novère et al., 2005) has been established to guide such curation and is equally applicable to whole-cell electrophysiology models but has not yet been widely applied in this area. In order to be able to curate an implementation of an electrophysiology model it is essential to have an authoritative version of the model against which the implementation can be critically evaluated. In the MIRIAM standard this is referred to as the model's reference description and here we put forward a standard suitable for defining reference descriptions of cellular electrophysiology models.
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2 APPROACH |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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CellML (http://www.cellml.org) has previously been shown as a versatile tool for the definition (Nickerson and Hunter, 2006) and utilization (Nickerson et al., 2006) of cellular electrophysiology models. As such, we use CellML for the base definition of the mathematical model and use CellML related technology in the definition of a reference description. The same technology could, however, be applied equally well to mathematical models specified in other standard formats, most notably SBML (http://sbml.org) (Hucka et al., 2003). A preliminary example demonstrating such integration is available online with the Supplementary information.
The key requirement for a reference description is the ability to unambiguously annotate very specific aspects of the mathematical model and to ensure that the model is sufficiently well annotated that it can be quantitatively interpreted. In the following section we describe how this can be achieved in regard to cellular electrophysiology models through the application of two developing metadata specifications from the CellML community, namely simulation and graphing metadata. These two metadata specifications are being actively developed within the CellML community and we make use of the current specification drafts available from http://www.cellml.org (version draft-graph-metadata-02 of the graphing metadata and dated August 23, 2006 for the simulation metadata specification).
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3 METHODS |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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CellML defines a standard language for encoding mathematical models in a machine-readable, software-independent format. By virtue of being an XML language, every resource in a CellML model can define a document-unique id attribute which is used in creating a world-unique URI for every resource within a CellML model. The unique URIs allow unambiguous annotation of any resource defined in a CellML model (true for any XML-based format, e.g., SBML). The primary resources defined in a CellML model are mathematical equations and the variables required in the equations.
A simply annotated CellML model goes a long way toward the definition of a reference description of a model. Through annotations such as literature citations and simple text comments, justification for parameter values and various mathematical formulae can be provided and linked explicitly to the corresponding resource within the model. In general, however, the model needs to be applied to specific scenarios in order to illustrate its validity. This requires the mathematical model to be fully parametrized and specific numerical simulations to be performed.
CellML simulation metadata (http://www.cellml.org/specifications/meta-data/simulations) attempts to define sufficient information to enable specific simulations to be completely defined in a reproducible, machine-readable manner. Thus, annotation of CellML models with simulation metadata allows the actual application of the mathematical model to a specific scenario to be unambiguously defined. The last step required is the processing of the data generated from the numerical simulations as defined by simulation metadata.
CellML graph metadata (http://www.cellml.org/specifications/metadata/graphs) provides the link between raw-simulation output and a more human-readable representation of that data. While the primary purpose of graph metadata is to define an unambiguous graphical representation of specific simulation results, at the most general level it also provides a mechanism to extract specific subsets of data from potentially many simulations based on many different underlying CellML models. As such, the graph metadata provides the foundation for a quantitative evaluation of the model implementation. In addition, graph metadata allows for the annotation of simulation data with specific experimental observations and thus provides a mechanism to explicitly relate model outputs to experimental data.
In combination, these technologies provide the required building blocks for the definition of complete reference descriptions of cellular electrophysiology models. Figure 1 graphically illustrates the workflow we propose as the basis of defining a reference description. The reference description is a collection of graphing metadata which defines which simulations need to be performed, how the simulation results are processed and analyzed, and any links to experimental data. Each simulation description defines the actual mathematical model and the numerical methods used to perform the simulation. At this stage the model description is instantiated into some form suitable for numerical simulation, ensuring that the mathematical model is well defined and all required parameters and boundary conditions are specified.
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Performing the numerical simulations results in the output data [1], which is explicitly linked to resources in the mathematical models by the resource URIs. As defined by the graphing metadata, a subset of the entire simulation output data is created [2], which can then be further analyzed or filtered (particular time slices could be extracted, for example) resulting in the final dataset [3]. At this stage the simulation outputs may also be compared directly to external data as a test of either the model validity or the correctness of the mathematical model implementation. For model implementation and software testing purposes the external data is likely to be that generated by the original model implementation whereas for actual model validity checks the data will be actual experimental observations. Finally, the graphical representation [4] can be produced from the final dataset [3] for inclusion in both the reference description documentation and potentially the final peer reviewed publication of the model.
We have developed a software tool, CellMLSimulator, for use in the development and testing of this reference description framework. CellMLSimulator is an open source tool available from http://cellml.sourceforge.net.
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4 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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An initial example of this standard in practice is available at http://www.bioeng.nus.edu.sg/compbiolab/p2/, where we have created a reference description for parts of the Corrias and Buist (2007) gastric smooth muscle cellular electrophysiology model. In this initial demonstration we present reference descriptions of two transmembrane ionic currents, which include literature citations for most model parameters, species and biological entity annotation where known, as well as documented equations. In one example we include both the experimental data used to fit part of the model and an independent dataset illustrating the suitability of the fitted relationship.
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5 CONCLUSION |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Through adoption of this standard approach to defining an original reference description for mathematical models of cellular electrophysiology model, authors will be making their models available to other scientists in a format that is both easy to reuse and extend and, most importantly, easy to validate against. The traditional peer reviewed journal article is then written based on this reference description allowing the author to focus on the scientific discoveries encompassed by the model while providing all the glorious mathematical, implementation, and validation details through supplementing the article with the reference description.
The primary limitation currently seen as blocking mass adoption of this approach to the definition of model descriptions is the lack of user-friendly tools for the addition and modification of such annotation of mathematical models. Annotation of the example models used in the online supplement was achieved by manual editing of the XML source documents, which obviously presents a huge stumbling block for most model authors and curators. At time of writing, there is one graphical user interface which provides the capability of viewing and editing graphing and simulation metadata – PCEnv.1 Better metadata support in the CellML API2 is an ongoing project, which will allow application developers to more easily incorporate CellML community standards into their software projects. CellMLSimulator is an early example of such an application.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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A*STAR BMRC Grant #05/1/21/19/383.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: Olga Troyanskaya
1 http://www.cellml.org/tools/pcenv 
2 http://www.cellml.org/tools/api
Received on December 13, 2007; revised on February 5, 2008; accepted on February 27, 2008
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REFERENCES |
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TOPABSTRACT1 INTRODUCTION2 APPROACH3 METHODS4 RESULTS5 CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Corrias A, Buist ML. A quantitative model of gastric smooth muscle cellular activation. Ann. Biomed. Eng. (2007) 35:1595–1607.[CrossRef][Web of Science][Medline]
Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (1952) 117:500–544.
Hucka M, et al. The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics (2003) 19:524–531.
Le Novére N, et al. Minimum information requested in the annotation of biochemical models (miriam). Nat. Biotechnol. (2005) 23:1509–1515.[CrossRef][Web of Science][Medline]
Nickerson DP, Hunter PJ. The Noble cardiac ventricular electrophysiology models in CellML. Prog. Biophys. Mol. Biol. (2006) 90:346–359.[CrossRef][Web of Science][Medline]
Nickerson DP, et al. Computational multiscale modeling in the IUPS Physiome Project: modeling cardiac electromechanics. IBM J. Res. & Dev. (2006) 50:617–630.
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