[Show abstract][Hide abstract] ABSTRACT: Exposed to a sufficiently high extracellular potassium concentration ([K( + )]₀), the neuron can fire spontaneous discharges or even become inactivated due to membrane depolarisation ('depolarisation block'). Since these phenomena likely are related to the maintenance and propagation of seizure discharges, it is of considerable importance to understand the conditions under which excess [K( + )]₀ causes them. To address the putative effect of glial buffering on neuronal activity under elevated [K( + )](o) conditions, we combined a recently developed dynamical model of glial membrane ion and water transport with a Hodgkin-Huxley type neuron model. In this interconnected glia-neuron model we investigated the effects of natural heterogeneity or pathological changes in glial membrane transporter density by considering a large set of models with different, yet empirically plausible, sets of model parameters. We observed both the high [K( + )]₀-induced duration of spontaneous neuronal firing and the prevalence of depolarisation block to increase when reducing the magnitudes of the glial transport mechanisms. Further, in some parameter regions an oscillatory bursting spiking pattern due to the dynamical coupling of neurons and glia was observed. Bifurcation analyses of the neuron model and of a simplified version of the neuron-glia model revealed further insights about the underlying mechanism behind these phenomena. The above insights emphasise the importance of combining neuron models with detailed astroglial models when addressing phenomena suspected to be influenced by the astroglia-neuron interaction. To facilitate the use of our neuron-glia model, a CellML version of it is made publicly available.
[Show abstract][Hide abstract] ABSTRACT: MOTIVATION: The Physiome Model Repository 2 (PMR2) software was created as part of the IUPS Physiome Project (Hunter and Borg, 2003), and today it serves as the foundation for the CellML model repository. Key advantages brought to the end user by PMR2 include: facilities for model exchange, enhanced collaboration and a detailed change history for each model. AVAILABILITY: PMR2 is available under an open source license at http://www.cellml.org/tools/pmr/; a fully functional instance of this software can be accessed at http://models.physiomeproject.org/.
[Show abstract][Hide abstract] ABSTRACT: MOTIVATION: The Physiome Project was established in 1997 to develop tools to facilitate international collaboration in the physiological sciences and the sharing of biological models and experimental data. The CellML language was developed to represent and exchange mathematical models of biological processes. CellML models can be very complicated, making it difficult to interpret the underlying physical and biological concepts and relationships captured/described in the mathematical model. RESULTS: To address this issue a set of ontologies was developed to explicitly annotate the biophysical concepts represented in the CellML models. This article presents a framework that combines a visual language, together with CellML ontologies, to support the visualization of the underlying physical and biological concepts described by the mathematical model and also their relationships with the CellML model. Automated CellML model visualization assists in the interpretation of model concepts and facilitates model communication and exchange between different communities.
[Show abstract][Hide abstract] ABSTRACT: Calcium ions are the most ubiquitous and versatile signaling molecules in eukaryotic cells. Calcium homeostasis and signaling systems are crucial for both the normal growth of the budding yeast Saccharomyces cerevisiae and the intricate working of the mammalian heart. In this paper, we make a detailed comparison between the calcium homeostasis/signaling networks in yeast cells and those in mammalian cardiac myocytes. This comparison covers not only the components, structure and function of the networks but also includes existing knowledge on the measured and simulated network dynamics using mathematical models. Surprisingly, most of the factors known in the yeast calcium homeostasis/signaling network are conserved and operate similarly in mammalian cells, including cardiac myocytes. Moreover, the budding yeast S. cerevisiae is a simple organism that affords powerful genetic and genomic tools. Thus, exploring and understanding the calcium homeostasis/signaling system in yeast can provide a shortcut to help understand calcium homeostasis/signaling systems in mammalian cardiac myocytes. In turn, this knowledge can be used to help treat relevant human diseases such as pathological cardiac hypertrophy and heart failure.
FEMS Yeast Research 08/2009; 9(8):1137-47. DOI:10.1111/j.1567-1364.2009.00552.x · 2.82 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: MOTIVATION: CellML is an implementation-independent model description language for specifying and exchanging biological processes. The focus of CellML is the representation of mathematical formulations of biological processes. The language captures the mathematical and model building constructs well, but does not lend itself to capturing the biology these models represent. RESULTS: This article describes the development of an ontological framework for annotating CellML models with biophysical concepts. We demonstrate that, by using these ontological mappings, in combination with a set of graph reduction rules, it is possible to represent the underlying biological process described in a CellML model.
[Show abstract][Hide abstract] ABSTRACT: The development of standards for encoding mathematical models is an important component of model building and model sharing among scientists interested in understanding multi-scale physiological processes. CellML provides such a standard, particularly for models based on biophysical mechanisms, and a substantial number of models are now available in the CellML Model Repository. However, there is an urgent need to extend the current CellML metadata standard to provide biological and biophysical annotation of the models in order to facilitate model sharing, automated model reduction and connection to biological databases. This paper gives a broad overview of a number of new developments on CellML metadata and provides links to further methodological details available from the CellML website.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 06/2009; 367(1895):1845-67. DOI:10.1098/rsta.2008.0310 · 2.15 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Author Summary
A key experimental observation associated with the astroglia–neuron interaction is the shrinkage of the extracellular space (ECS) that occurs in response to enhanced neuronal activation. Although well documented to be present in mammalian brains, this phenomenon has resisted a proper explanation since it was first reported. We present here a mathematical conceptualization that may explain the main mechanisms behind ECS shrinkage and provide a framework for a theoretical-experimental research programme that may help to reach a consensus explanation. Effective clearance of K+ is essential for normal brain function because an inappropriate increase in extracellular K+ will enhance neuronal excitability and promote neuronal afterdischarges and increase the probability of epileptic episodes. The shrinkage of the ECS usually appears in conjunction with K+ clearance and must be taken into account in a model of how astrocytes clear excess K+ following trains of action potentials. The present model allows us to make several clear and testable predictions addressing the relationship among potassium clearance, water transport, and ECS shrinkage. Among these are predictions concerning water transport functions of aquaporins in astrocytes, involvement of cotransporters in potassium clearance, and effects of particular knockouts on ECS shrinkage and ion concentrations.
[Show abstract][Hide abstract] ABSTRACT: The CellML language was developed in response to the need for a high-level language to represent and exchange mathematical models of biological processes. The flexible structure of CellML allows modellers to construct mathematical models of the same biological system in many different ways. However, some modelling styles do not naturally lead to clear abstractions of the biophysical concepts and produce CellML models that are hard to understand and from which it is difficult to isolate parts that may be useful for constructing other models. In this article, we advocate building CellML models which isolate common biophysical concepts and, using these, to build mathematical models of biological processes that provide a close correspondence between the CellML model and the underlying biological process. Subsequently, models of higher complexity can be constructed by reusing these modularized CellML models in part or in whole. Development of CellML models that best describe the underlying biophysical concepts thus avoids the need to code models from scratch and enhances the extensibility, reusability, consistency and interpretation of the models.
[Show abstract][Hide abstract] ABSTRACT: Many phenomenological models of cerebral aneurysm formation have been proposed. Such studies have focused on modeling the
structural adaption of the arterial wall. However, further development is required to accurately represent the underlying
mechanobiology during growth and remodeling processes. Here, we present a general framework for modeling the interplay of
fluid dynamics, molecular signaling pathways and arterial wall mechanics.
[Show abstract][Hide abstract] ABSTRACT: The zinc homeostasis system in Escherichia coli is one of the most intensively studied prokaryotic zinc homeostasis systems. Its underlying regulatory machine consists of repression on zinc influx through ZnuABC by Zur (Zn2+ uptake regulator) and activation on zinc efflux via ZntA by ZntR (a zinc-responsive regulator). Although these transcriptional regulations seem to be well characterized, and there is an abundance of detailed in vitro experimental data available, as yet there is no mathematical model to help interpret these data. To our knowledge, the work described here is the first attempt to use a mathematical model to simulate these regulatory relations and to help explain the in vitro experimental data.
We develop a unified mathematical model consisting of 14 reactions to simulate the in vitro transcriptional response of the zinc homeostasis system in E. coli. Firstly, we simulate the in vitro Zur-DNA interaction by using two of these reactions, which are expressed as 4 ordinary differential equations (ODEs). By imposing the conservation restraints and solving the relevant steady state equations, we find that the simulated sigmoidal curve matches the corresponding experimental data. Secondly, by numerically solving the ODEs for simulating the Zur and ZntR run-off transcription experiments, and depicting the simulated concentrations of zntA and znuC transcripts as a function of free zinc concentration, we find that the simulated curves fit the corresponding in vitro experimental data. Moreover, we also perform simulations, after taking into consideration the competitive effects of ZntR with the zinc buffer, and depict the simulated concentration of zntA transcripts as a function of the total ZntR concentration, both in the presence and absence of Zn(II). The obtained simulation results are in general agreement with the corresponding experimental data.
Simulation results show that our model can quantitatively reproduce the results of several of the in vitro experiments conducted by Outten CE and her colleagues. Our model provides a detailed insight into the dynamics of the regulatory system and also provides a general framework for simulating in vitro metal-binding and transcription experiments and interpreting the relevant experimental data.
BMC Systems Biology 11/2008; 2(1):89. DOI:10.1186/1752-0509-2-89 · 2.44 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The CellML Model Repository provides free access to over 330 biological models. The vast majority of these models are derived from published, peer-reviewed papers. Model curation is an important and ongoing process to ensure the CellML model is able to accurately reproduce the published results. As the CellML community grows, and more people add their models to the repository, model annotation will become increasingly important to facilitate data searches and information retrieval. AVAILABILITY: The CellML Model Repository is publicly accessible at http://www.cellml.org/models.
[Show abstract][Hide abstract] ABSTRACT: Macrophages have traditionally been identified in murine tissues using a small range of markers, typically F4/80, CD68 and CD11b. However many studies have suggested that substantial heterogeneity exists in macrophage populations, and no single marker, nor even pair of markers, can necessarily identify all the populations. Further, many of the key monoclonal antibodies have been raised in the same species, making it difficult to combine them in histochemical studies. Here we have optimised a triple colour immunofluorescent staining protocol, utilising an anti-FITC technique, to allow antibodies to macrophage markers to be used simultaneously. We highlight the substantial heterogeneity of cells in both normal liver and spleen that stain for F4/80, CD68, CD11b, and CD11c. Using diet-induced steatohepatitis as a model of liver inflammation, we show that CD11b is expressed by newly migrating macrophage precursors, but is an unreliable marker for macrophage precursors when used alone because it is also expressed by migrating neutrophils. In healthy livers CD11c expression is a unique feature of a population of cells immediately surrounding the sinusoids. However, during hepatic inflammation CD11c can also be co-expressed by other cells, including both infiltrating cells and F4/80+ cells within the liver parenchyma. While no one marker alone is sufficient to account for all macrophage populations, we confirm that F4/80 marks the majority of the tissue-resident macrophages in both the liver and the spleen, although F4/80- populations that are positive for CD68, CD11b, or CD11c also exist. Distinguishing between tissue macrophages and dendritic cells with these markers remains problematic.
[Show abstract][Hide abstract] ABSTRACT: The CellML repository now contains a number of well curated CellML models of cardiac biology and physiology at the cellular and subcellular level. Recently this resource has been growing rapidly in both quality and quantity and includes models of cardiac electrophysiology, excitation-contraction coupling, myofilament mechanics, signalling systems and combinations thereof. Herein we describe the CellML model repository, its range of models, the tools used to develop and test these models and the processes and aims of curating them. The relevance of this resource to multi-scale modelling of the heart in the present and the future is then discussed. Poster presented at Waiheke 2008 Multiscale Modelling of the Heart Workshop.
[Show abstract][Hide abstract] ABSTRACT: Advances in biotechnology and experimental techniques have lead to the elucidation of vast amounts of biological data. Mathematical models provide a method of analysing this data; however, there are two issues that need to be addressed: (1) the need for standards for defining cell models so they can, for example, be exchanged across the World Wide Web, and also read into simulation software in a consistent format and (2) eliminating the errors which arise with the current method of model publication. CellML has evolved to meet these needs of the modelling community. CellML is a free, open-source, eXtensible markup language based standard for defining mathematical models of cellular function. In this paper we summarise the structure of CellML, its current applications (including biological pathway and electrophysiological models), and its future development--in particular, the development of toolsets and the integration of ontologies.
Progress in Biophysics and Molecular Biology 06/2004; 85(2-3):433-50. DOI:10.1016/j.pbiomolbio.2004.01.004 · 2.27 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: CellML is an XML-based exchange format developed by the University of Auckland in collaboration with Physiome Sciences, Inc. CellML 1.1 has a component-based architecture allowing a modeller to build complex systems of models that expand and reuse previously published models. CellML Metadata is a format for encoding contextual information for a model. CellML 1.1 can be used in conjunction with CellML Metadata to provide a complete description of the structure and underlying mathematics of biological models. A repository of over 200 electrophysiological, mechanical, signal transduction, and metabolic pathway models is available at www.cellml.org.
SIMULATION: Transactions of The Society for Modeling and Simulation International 12/2003; 79(12):740-747. DOI:10.1177/0037549703040939 · 0.82 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: CellML v1.1 is a human and machine-readable model exchange protocol with a proven track record in representing Systems and Synthetic Biology models. The language is highly modular and flexible, encouraging innovation but also allowing divergent styles of model encoding. This can lead to incompatibilities between models, making combination and reuse difficult. The CellML Repository makes hundreds of models publically available which are constructed according to many different styles. Various groups have separately proposed guidelines for representing electrophysiology[5,6], signalling[7,8], and gene regulation models in CellML. A consistent, common set of guidelines across sub-domains is needed to enhance modular model construction and interoperability.
We therefore aim to provide a set of guidelines that researchers in any sub-domain can use to construct CellML models which are consistently clear, reusable, maintainable and extensible. A group of key researchers from the above initiatives and associated tool development[9,10] collaborated during facilitated sessions to develop a set of guidelines. We then tested these by encoding signalling, electrophysiology and gene regulation systems, and constitutive material laws. We provide guidelines for forming and reusing common mathematical forms, providing parameters and initial conditions, structuring modular components for maximum extensibility, and on the minimum level of semantic annotation to include. These best practices are illustrated with examples now represented in a modular, consistent manner.
These practices enhance the extensibility, clarity and maintainability of CellML models, providing guidance to both new and experienced users. In addition, the use of a common style will simplify the process of combining domain-specific models. Finally, the inherently modular style combined with semantic annotation will encourage the construction of libraries of modules, which can be recombined to address more complex biomedical scenarios than previously tackled.
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[Show abstract][Hide abstract] ABSTRACT: This document specifies CellML 1.1, an XML-based language for describing and exchanging models of cellular and subcellular processes. MathML embedded in CellML documents is used to define the underlying mathematics of models. Models consist of a network of re-usable components, each with variables and equations manipulating those variables. Models may import other models to create systems of increasing complexity. Metadata may be embedded in CellML documents using RDF.