The specification of SBML Level 1 is freely available from http://www.sbml.org/

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.

The CellML Model Repository is publicly accessible at http://www.cellml.org/models.

Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization -from proteins to cells, tissues, organs and organ systems -these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline.

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Organ function (the heart beat for example) can only be understood through knowledge of molecular and cellular processes within the constraints of structure-function relations at the tissue level. A quantitative modeling framework that can deal with these multiscale issues is described here under the banner of the International Union of Physiological Sciences Physiome Project.

CellML tm is an XML-based language designed to facilitate the exchange of biological models across the World Wide Web. Processing applications are able to appropriately render models based on the definition of model structure given in a CellML document, and run simulations based on the definition of the underlying mathematics.CellML is designed to be a general framework upon which a wide variety of models may be built. The basic constituents and structure are simple, providing a common basis for describing models and facilitating the creation of complex models from simpler ones by combining models and/or adding detail to existing models.CellML models are represented as a collection of discrete components linked by connections to form a network. A component is a functional unit that may correspond to a physical compartment, a collection of entities engaged in similar tasks, or a convenient modelling abstraction. Components may contain variables, mathematical relationships that specify the interactions between those variables, and metadata. Variables may be local to a component, or made visible to other components via interface attributes. All interactions between variables within a component are described using MathML content markup. The interface attributes describe the external view of the component, specifying those variables visible to other components. A connection is a directed mapping from externally visible variables in one component to those of another. Every variable has a set of units associated with it, making it possible to connect together components with variables defined using different units.CellML offers additional facilities, such as metadata, for adding context information to a model, and component grouping. These assist in the creation and maintenance of models but do not alter the mathematics of the model. All models described using CellML can be reduced to the canonical form: a set of connected components.

The heat liberated upon stress production in isolated cardiac muscle provides insights into the complex thermodynamic processes underlying mechanical contraction. To that end, we simultaneously measured the heat and stress (force per cross-sectional area) production of cardiac trabeculae from rats using a flow-through micromechanocalorimeter. In a flowing stream of O2-equilibrated Tyrode solution (ϳ22°C), the stress and heat production of actively contracting trabeculae were varied by 1) altering stimulus frequency (0.2-4 Hz) at optimal muscle length (Lo), 2) reducing muscle length below Lo at 0.2 and 2 Hz, and 3) changing extracellular Ca 2ϩ concentrations ([Ca 2ϩ ]o; 1 and 2 mM). Linear regression lines were adequate to fit the active heat-stress data. The active heat-stress relationships were independent of stimulus frequency and muscle length but were dependent on [Ca 2ϩ ]o, having greater intercepts at 2 mM [Ca 2ϩ ]o than at 1 mM [Ca 2ϩ ]o (3.5 and 2.0 kJ·m Ϫ3 ·twitch Ϫ1 , respectively). The slopes among the heat-stress relationships did not differ. At the highest experimental stimulus frequency, pronounced elevation of diastolic Ca 2ϩ resulted in incomplete twitch relaxation. The resulting increase of diastolic stress, which occurred with negligible metabolic energy expenditure, subsequently diminished due to the time-dependent loss of myofilament Ca 2ϩ -sensitivity.cardiac thermodynamics; heat-stress relationships; dynamic stiffness; diastolic calcium, myofilament calcium sensitivity WHEN AN ISOLATED CARDIAC MUSCLE, held fixed at both ends, is electrically stimulated, twitch force is produced. A consequence of this mechanical contraction is the simultaneous liberation of heat. Thus, the relationship between heat and stress (force per cross-sectional area) production provides insights into the complex thermomechanical processes occurring within the muscle. In selecting suitable isolated multicellular tissue preparations for in vitro experiments, two important criteria have to be met. First, for an unambiguous interpretation of stress production, the myocytes should be aligned in parallel with the direction of force measurement. Second, to avoid the risk of tissue anoxia, the preparation should be sufficiently small in radial dimension for O 2 to diffuse into the muscle core under high rates of O 2 demand. The first criterion can be achieved using either papillary muscles or cardiac trabeculae. Compared with papillary muscles, cardiac trabeculae have cross-sectional areas an order of magnitude smaller. Thus, to satisfy the second criterion, cardiac trabeculae are preferable, owing to their minute radial dimensions (about that of a human hair), which greatly facilitates the diffusion of O 2 .Using a flow-through micromechanocalorimeter (11), we simultaneously measured the heat and stress production of cardiac trabeculae excised from the right ventricles of rat hearts. Optimized in vitro metabolic conditions were achieved by continuous provision of O 2 and removal of waste products, enabling measureme...